Derivatives Definition and 1000 Threads

Hi Everyone, I was studying coordinate transformation and I came across this equation, that I couldn't understand how it came up. Let me put it this way: x = rcosθ Then if I want to express the partial derivative (of any thing) with respect to x, what would be the expression? i.e. ∂/∂x=...

I'm reading through the book Quantum Mechanics (Second Edition) by David J. Griffiths and it got to the part about proving that if you normalise a wave function, it stays normalised (Page 13). That part that I don't get is how they say: ## \dfrac{i \hbar}{2m} \left( \Psi^* \dfrac{\partial^2...

So I have an exam tomorrow, and the teacher provided a review. f(x) = ln(x + y) I remember that d/dx ln[f(x)] = f'(x)/f(x) so would that not equal 2/(x + y) ? The answer she gave is 1/(x + y - 1) ... where that neg. one came from I have no idea. Come to think of it, there were no...

Homework Statement Find an equation of the tangent line at the point indicated f(x) = 5x2-2x+9 , x = 1 Homework Equations (d/dx) bx = ln(b)bx General Power Rule which states: (d/dx) g(x)n = n(g(x))n-1 * g'(x) The Attempt at a Solution So looking at a previous problem...

So in my math class we're studying derivatives involving ln(), tanh, coth, etc.. I need to say this first. I skipped precalc and trig and went straight to calculus, so whenever I see a trig problem, I can only go off of what I've learned "along the way." This problem has baffled me, please...

Hello MHB, I got one question, I was looking at a Swedish math video for draw graph and for some reason he did take derivate and did equal to zero and did calculate the roots and then he did take limit of the derivate function to the roots and it's there I did not understand, what does that...

Homework Statement f(x) is given by the forumula y=\sqrt{3x^2 + 2x + 1} Find A: The first derivative B: The second derivative Homework Equations chain rule quotient and product rule?The Attempt at a Solution I think I have made a good logical attempt at part A but only have an inclin when it...

I'm thinking in particular about Lenny Susskind's lectures, but I've seen other lecturers do it too. They'll be writing equation after equation using the partial derivative symbol: \frac{\partial f}{\partial a} And then at some point they'll realize that some problem they're currently...

Hello, Given is the function f = f(a,b,t), where a=a(b) and b = b(t). Need to express first and second order derivatives. \frac{\partial f}{\partial a} and \frac{\partial f}{\partial b} should be just that, nothing more to it here, correct? But \frac{df}{dt} = \frac{\partial...

Homework Statement Differentiate f(x) = x^{1/2} - x^{1/3} Homework Equations f(x) = f'(x)- g'(x) The Attempt at a Solution I am a little stuck about what to do after the first couple steps. Here is my attempt. f(x) = x^{1/2} - x^{1/3} f'(x) = (x^{1/2})' -(x^{1/3})' =...

Homework Statement Differentiate f(x) = (x^2 - 3x)^2 Homework Equations f'(x) = nf'(x)f(x)^(n-1) The Attempt at a Solution f’(x) = 2(x2-3x)’(x2-3x)2-1 = 2(2x-3)(x2-3x)1 = 2(2x3 – 6x2 – 3x2 + 9x) = 2(2x3 – 9x2 + 9x) = 4x3 – 18x2+ 18x Is this correct?

Homework Statement Expand x/(x-1) at a=1 The book already gives the expansion but it doesn't explain the process. The expansion it gives is: x/(x-1) = (1+x-1)/(x-1) = (x-1)^(-1) + 1 Homework Equations The Attempt at a Solution I've already solved for the Mclaurin expansion for the same...

Derivatives of inverse functions--how two formulas relate? Homework Statement I know two formulas for calculating the derivative of an inverse function, both of which I know how to derive, but I don't know how to relate them to one another. Homework Equations...

I've had to hit my books to help someone else. Ugh. Say we have the coordinate transformation \bf{x}' = \bf{x} + \epsilon \bf{q}, where \epsilon is constant. (And small if you like.) Then obviously d \bf{x}' = d \bf{x} + \epsilon d \bf{q}. How do we find \frac{d}{d \bf{x}'}? I'm missing...

Homework Statement Let f(x) = 2x2 -3x -5. Show that the slope of the secant line through (2, f(2)) and (2+h, f(2+h)) is 2h + 5. Then use this formula to compute the slope of : (a) The secant line through (2, f(2)), and (3, f(3)) (b) The tangent line at x = 2 (by taking a limit)...

Homework Statement The separation of layers is considered to occur at the thermocline, which is defined as the location of the steepest slope in the temperature gradient. Mathematically, this occurs at the inflection point – so the position of the thermocline can be found from the following...

For some polynomial functions it is useful to logarithmize both sides of the eq. First. How can this be applied for inverse trig functions? Is it even possible?

1. Is this the only example of a function ##f(x) \in C^1([0,1])## with discontinuous derivative $$f(x) = \begin{cases} x^2 sin(\frac{1}{x}) & \textrm{ if }x ≠ 0 \\ 0 & \textrm{ if }x = 0 \\ \end{cases}$$ It seems this example is over-used. Do we have other examples besides this one in...

Homework Statement If z=f(x,y) with u= x^2 -y^2 and v=xy , find the expression for (∂x/∂u). the (∂x/∂u) will be used to calsulate ∂z/∂u. my question is how to find (∂x/∂u). I don't know what to keep constant. Maybe the question has some problem. The answer is (∂x/∂u)=(x/2)/(x^2+y^2)...

Homework Statement We want to make a conical drinking cup out of paper. It should hold exactly 100 cubic inches of water. Find the dimensions of a cup of this type that minimizes the surface area. Homework Equations SA = pi*r^2 + pi*r*l where l is the slant height of the cone. V =...

Hi, I've recently taken a Calculus 1 (Differential Calculus) course and I've been looking ahead to see what sort of material is covered in the Calculus 2 (Integral Calculus) course. I am wondering about the relationship between derivatives and integrals. From what I understand, an integral...

Hello guys! Lately I've been studying some topics in Physics which require an extensive use vector calculus identities and, therefore, the manipulation of partial redivatives of vectors - in particular of the position and velocity vectors. However, I am not sure if my understanding of partial...

Homework Statement Where T(x,t)=T_{0}+T_{1}e^{-\lambda x}\sin(\omega t-\lambda x) \omega = \frac{\Pi}{365} and \lambda is a positive constant. Show that T satisfies T_{t}=kT_{xx} and determine \lambda in terms of \omega and k. I'm not to sure what is meant by the latter part of "determine...

f(z,t)=\frac{A}{b(z-vt)^{2}+1}... \frac{\partial^{2} f(z,t)v^{2} }{\partial z^2}=\frac{-2Abv^{2}}{[b(z-vt)^{2}+1]^{2}}+\frac{8Ab^{2}v^{2}(z-vt)^{2}}{[b(z-vt)+1]^{3}}=\frac{\partial^2 f}{\partial t^2} \frac{-2Abv^{2}}{[b(z-vt)^{2}+1]^{2}}+\frac{8Ab^{2}v^{2}(z-vt)^{2}}{[b(z-vt)+1]^{3}} this...

Homework Statement An object is traveling along a linear path according to the equation s(t) = 4t^3 - 3t^2 + 5 where t is measured in seconds and s(t) measured in meters. How far has the object traveled when its acceleration is zero? Homework Equations The Attempt at a Solution...

Newton's laws says ## F=ma ##. Which, as far as I can see, states that all physical interactions concern the second time derivative of position. And because there is no other way for two bodies to interact in the physical world, the "worst" I can do to a system is change its acceleration, right...

I have z=(e^y)φ*[y*e^(x^2/2y^2)].I have to prove that y*(dz/dx) -x*(dz/dy)=0.First of all what does φ mean there?

Hi, here I come again now with a problem, this time is more because the boo didn't really explain much deeper than the minimum. This time it's not homework related ... Yet. Lol. I just wanted to know how I would separate an equation like y=sin^2x cos3x To find the derivativ; I guess how...

Homework Statement Homework Equations I can't think of much. u(x,y) is harmonic, so its double derivatives with respect to x and y add up to zero. I'm not 100% sure, but does being harmonic also imply that u satisfies the cauchy riemann equations? That might come in handy in the...

Here's an example from my homework. I already turned it in, though. I basically just copied what I could from my notes, but I have no idea how this is done. Could someone explain this to me? I can't find anything intelligible (at least to me) of this stuff on any website. My notes contain parts...

Would anyone here know where I could find some kind of tutorial that goes step by step of how to evaluate functional derivatives? I'm looking over my notes, trying to make sense of this functional derivatives stuff the teacher did in class, and it makes no sense at all. I'm not even in the realm...

Hello PH, This is my first post. I came here while studying partial derivatives and after clicking here and there for over 4hrs for an answer. While practicing the derivatives rules i came across the hideous quotient rule. I've solved around 20 fractional problems trying to find a decision...

The idea of varying one thing but keeping others constant is central in scientific analysis. People want to know, other things constant, the effect of taking vitamins, smoking or drinking alcohol, just as examples. Is the idea of the partial derivative analogous to scientific empiricism's...

We know that the first derivative represents the slope of the tangent line to a curve at any particular point. We know that the second derivative represents the concavity of the curve. Or, the first derivative represents the rate of change of a function, and the second derivative represents the...

Derivatives with Quotient Law Help! I have a test tomorow, any help is much appreciated! :) Homework Statement Dervive using the quotient rule: [(2-x)^3] / [(x+1)^2] My attempt: = [(x+1)^2 (3(2-x)^2)]-[(2-x)^3 2(x+1)] When I try expanding I get the wrong answer. The...

Homework Statement Which of the following satisfy (f^k)(x) = 0 for all k >= 6? a) f(x) = 7x^4 + 4 + x^-1 b) f(x) = sqrt(x) c) f(x) = x^(9/5) d) f(x) = x^3 - 2 e) f(x) = 1 - x^6 f) f(x) = 2x^2 + 3x^5 Homework Equations None, but given as a problem in a chapter where the topic is higher...

Hello, Today did me and my friend talked of derivate and he asked about some help. Then he asked me is it possible to derivate $y^3+5x^2=5x-2y$ and i was clueless how i derivate that. Is this difficoult to derivate?is it possible to do it?

Homework Statement This is not really a homework or a coursework question. But I got a warning that I should submit my post in this section of the website.. I'm just saying this because I don't know if the answer to my question is at all achievable. And if it is how I should go about trying to...

I have given a function g(t)=∇(f(x(t))) , f: IR³->IR and x: IR-> IR³ and want to express the first 3 derivatives with respect to time most simply. I thought that g'(t)=Hessian(f(x(t)))dx/dt but how do I get the further derivatives. is there any chance to express those in terms of taking the...

Here's a question. This formula seems to be the keystone of calculus. That seems to be what the calculus books say, and it makes sense to me, as a rank beginner. This equation is what makes the seeming magic of defining the slope of a dimensionless point on a curved slope possible. And...

Homework Statement Find the coordinates of the point(s) on the following curves where the second derivative is as stated. Homework Equations y= \frac{x^3}{12} and \frac{d^{2}y}{dx^{2}} = 1.5 The Attempt at a Solution I'm used to working with the first derivative. Would I need to...

Homework Statement For the heat equation u_{t}=\alpha^{2}u_{xx} for x\in\mathbb{R} and t>0, show that if u(x,t) is a strong solution to the heat equation, then u_{t} and u_{x} are also solutions. Homework Equations u_{t}=\alpha^{2}u_{xx} The Attempt at a Solution I've considered...

Homework Statement general course question Homework Equations N/A The Attempt at a Solution fx is a first order partial derivative fxy is a second order partial derivative fxyz is a third order partial derivative I understand that Clairaut's Theorem applies to second order...

f(x)=5x^3+6x^2-3x+lnx (lnx)`=1/x f(x)=2x^4+3x^2+ cosx (cosx)`=-sinxI know that if I only have x, like 3x, then x disappears (correct me if I'm wrong). So what happens with lnx if x disappears? Same thing with cosx. The lesson is extreme values of functions and i saw critical points mentioned...

I am utilitizing rotation vectors (or SORA rotations if you care to call them that) as a means of splitting 3D rotations into three scalar orthogonal variables which are impervious to gimbal lock. (see SO(3)) These variables are exposed to a least-squares optimization algorithm which...

In a thermodynamics question, I was recently perplexed slightly by some partial derivative questions, both on notation and on physical meaning. I believe my questions are best posed as examples. Suppose we have an equation, (\frac{\partial x(t)}{\partial t}) = \frac{1}{y}, where y is a...

Homework Statement Use the continuity and momentum conservation equations for a single species to construct the following "convective derivative" equation for the fluid velocity: \frac{\partial\vec{v}}{\partial t}+\vec{v}\cdot\nabla\vec{v}=\vec{g}-\frac{1}{\rho}\nabla p...

Homework Statement compute the following derivatives using the product rule and quotient rule as necessary, without using chain rule. Homework Equations d/dx ((sin(x))^2) The Attempt at a Solution =(sin(x))(sin(x)) =(cos(x))(sin(x))+(sin(x))(cos(x)) =2(sin(x))(cos(x))

Why do some functions not have Anti derivatives?? as the title says why are some functions like ## √cotx##(root cotx) not integratable??

Hi i have two questions: 1) When asked to prove \mathcal{L}_{u}\mathcal{L}_{v}W - \mathcal{L}_{v}\mathcal{L}_{u}W = \mathcal{L}_{[u,v]}. I achieved [u,v]w = \mathcal{L}_{[u,v]}. This was found by appliying a scalar field <b> to the LHS and simplifying and expanding using + and scalar...