Differentiate Definition and 227 Threads

We know that a = vdv/dx But is it applicable in only one dimensional components or is this actually a vector equation? If so then how do we exactly differentiate with respect to position 'vector'?

Hi, there. I am doing differentiation with respect to an affine parameter ##s##, I am not sure whether my idea is right or wrong. Let ##C## be a geodesic for light and the path length ##s## on it be the affine parameter. Now I need to calculate ##\frac {\partial f}{\partial s}##, with ##f##...

In my country, we get yearly rainfall from South-West Monsoon. But from time to time, there is something called cylonic (or western) disturbances which bring rain in my country. I have myself observed that though disturbances are cylconic, yet we (at my particular location and about 50km radius)...

Summary:: Differentiate an equation to get the minimum peak I have this equation: 6.3504 = 23.04 ( 1-141978.24XY)^2 + 141978.24X^2 I want to differentiate it with respect to X to get the minimum peak of Y . dy/dx =0 . See attached file Thanks for help [Moderator's note: moved from a...

Given the Bell State in Z basis ##\psi = (a\uparrow \downarrow - b\downarrow \uparrow )## where ##a^2+b^2=1##. Now Alice has one particle and sends the other to Bob. Suppose Alice decides to measure her particle in Z direction. Thus entanglement collapses. Query: 1. How do we know which...

I have a quantity of black, lustrous powder taken from inside a gas pipe. I want to know whether it's from copper pipe or from steel pipe. Is there a very simple test I can do? I'm not a chemist and have no specialist equipment.

Hello, good afternoon guys. I need a little help from you: D 1)n a positive integer. f(x)=x(1-x)^n Solve the equation f'(x)=0 in 0<x<1 this question I asked and found x = 1 / (x + 1) ok 2)An be the maximum value of f(x)=x(1-x)^n in [0,1] Calculate lim (n+1)an n tending to infinity the...

Thank you in advance :)

Is this correct?

I tried to find examples on the internet but I am still confused.

Hi guys, I am reading my lecture notes for Mechanics and Variations and I am trying to understand the maths here. From what I can see there we differentiated with respect to a derivative. Could you tell me how do we do that? Thanks

The equation of flow acceleration is where du/dt is the global acceleration, and ∂u/∂t and u ∂u/∂x are local and convective acceleration respectively. And the heat conduction equation is which is heat stored = net heat flux + heat generated. My question is: why does the ∂T/∂t part in the...

I have seen people talking about measuring Doppler shift of stars to know how fast they are receding from us. But if I measured say a particular frequency f, how do I know whether this is shifted frequency or just the emission?

I was reading a different post, https://www.physicsforums.com/threads/differntiating-a-circle.279719/#post-2003287 and was doing great... guys, thanks so much for this forum! HallsofIvy posted "1: You titled this "differentiation of a circle" which makes no sense. You cannot differentiate a...

Homework Statement How to differentiate between rectangular beam and flange beam ? In the question below , the answer provided is flange beam , I'm wondering can i design it as rectangular beam Homework EquationsThe Attempt at a Solution Since there's no clue whether the flange beam or...

Homework Statement Homework Equations [/B] I came over these Equations when I was Reading an article. I tried to replicate the results by differentiating Equation 9 w.r.t time. However I could not do it. Just to be sure. The growth of a variable is Equal to the time derivative of the same...

Hi, I am dealing with an equality of the form: f(x)=g(y,z) and I need to compute ##dx##. Is the following relation correct? dx={(\frac{\partial f}{\partial x})}^{-1}( \frac{\partial g}{\partial y}dy + \frac{\partial g}{\partial z}dz ) Thank you in advance.

Homework Statement How do we determine a specific force mentioned in a question to be conservative or non-conservative? 2. Relevant data Conservative force is a force whose work done does not depend on the path that is taken while doing it. Examples include electrostatic force, gravitational...

Is y''(x) same as d2y/dx2. As it's y''(x) so how do we find out y(x) and if it can be taken as a double derivative, i was having doubts in this. Double differentiation of y is equal to -y... e^ something maybe ? and sign should change ?

I remember reading on a blog or a news article on the internet once that sometimes counterfeiters have made fake silver coins and silver bars out of molybdenum. Silver is worth far more than molybdenum. Counterfeiters made fake silver out of molybdenum because they could acquire the molybdenum...

I'm working through the problems in Mary Boas's Mathematical Methods text. Here's how she began solving one problem... "We take differentials of the equation 1/i + 1/o = 1/f (f=constant) to get -di/i2 - do/o2 = 0." So on the left side the first term was differentiated with respect to i and...

What is the differential of infinity?

Homework Statement This is a problem from Dynamics but I'm mostly having trouble with the calculus. Derive an expression for the position, velocity, and acceleration of a machine in terms of: r, \dot {r}, θ, \dot{θ}, \ddot{r}, \ddot{θ}, . r = length of the arm θ = angle of the arm to the...

Good day, I try to differentiate GHZ-state and W-state using three tangle. Suppose The value three tangle for GHZ-state equal to 1 while W-state equal to 0. I used three tangle formula, $$\tau_{ABC}=\tau_{A(BC)}-\tau_{AB}-\tau_{AC}=2(\lambda^{AB}.\lambda^{AB}+\lambda^{AC}.\lambda^{AC})$$...

Hello, and thank you for your time. I just started my A-levels derivatives/differentiation , and I would be more than happy if you could help me clarify it. For example I know that y is a function in terms of x right? y=f(x) The derivative of it is f'(x)=dy/dx . This means it is the rate of...

Homework Statement a) Differentiate the following equation with respect to: 1) θ 2) Φ 3) ψ (Ua - Ub)' * C * r where: C is a 3 x 3 rotation matrix: [ cos θ cos ψ, -cos Φ sin ψ + sin Φ sin θ cos ψ, sin Φ sin ψ + cos Φ sin θ cos ψ] [ cos θ sin ψ, cos Φ cos ψ + sin Φ sin θ sin...

Homework Statement for d/dx(e^x) , the series should be start from 2 rather than 1 , right ? because when k = 1 , the circled part would become 0 , the series for (e^x) is 1 + x + ... Homework EquationsThe Attempt at a Solution

I cannot understand the first part (second line) where it says dw/dk Can someone explain in a more step by step method

Temperature of a system is defined as $$\left( \frac{\partial \ln(\Omega)}{ \partial E} \right)_{N, X_i} = \frac{1}{kT}$$Where Ω is the number of all accessible states (ways) for the system. Ω can only take discrete values. What does this mean from a mathematical perspective? Many people say we...

if we have two particle then how we differentiate between boson and fermion ,any experiment that differentiate them?

Hey guys, Im studying for an exam and don't fully understand the jacobian process. Speciffically how you can differential the middle colum with respect to theta_3. Please view attached. So from step 1 to 2. Thanks.

Homework Statement Given the potential energy function V(x,y)=V(ax-by) where a,b is an arbitrary constants differentiate with respect to x and y. Homework Equations Multivariavle differentiation The Attempt at a Solution The answer yields (d/dt)p1=-aV'(ax-by) (d/dt)p2=+bV'(ax-by). The right...

Homework Statement What is ##\frac{d}{dx}(cos^2 x)##? Homework EquationsThe Attempt at a Solution u = cos x ##\frac{du}{dx} = -\sin x## ##\frac{d}{dx}(cos^2 x) = \frac{d}{du}(u^2) \ \frac{du}{dx}## ##= 2u \ \frac{du}{dx}## ##= 2 \cos x (-\sin x)## ##= -2 \cos x \sin x## Is it correct?

Homework Statement A ball is dropped from a height of 100 ft, at which time its shadow is 500 ft from the ball. How fast is the shadow moving when the ball hits the ground? The ball falls with velocity 32 ft/sec, and the shadow is cast by the sun.If i draw this in a cartesian cordinate...

If two cars are traveling either in parallel or in close succession to one another how can a laser determine which car it is gauging the speed of?

Hello! (Wave) The differential equation $xy''+(1-x)y'+ay=0, a \in \mathbb{R}$, that is called equation Laguerre, is given. Let $L_n$ be the polynomial $L_n(x)=e^x \frac{d^n}{dx^n} (x^n \cdot e^{-x})$ (show that it is a polynomial), $n=1,2,3, \dots$. Show that $L_n$ satisfies the equation...

Homework Statement Solve ∂v/∂θ and ∂v/∂r. (refer to attached image for equations) Homework Equations Refer to attached image. note that the velocity is expressed in cylindrical coordinates and attention must be paid to the directional unit vectors eθ and eρ.[/B] The Attempt at a Solution...

Homework Statement for example: ##\frac{\partial(F^{ab}F_{ab})}{ \partial g^{ab}} ## where F_{ab} is electromagnetic tensor. or ##\frac{\partial N_{a}}{\partial g^{ab}}## where ##N_{a}(x^{b}) ## is a vector field. Homework EquationsThe Attempt at a Solution i saw people write ##F^{ab}F_{ab}##...

Homework Statement (a) Find the christoffel symbols (Done). (b) Show that ##\phi## is a solution and find the relation between A and B.[/B] Homework EquationsThe Attempt at a Solution Part(b) \nabla_\mu \nabla^\mu \phi = 0 I suppose for a scalar field, this is simply the normal derivative...