Differentiation Definition and 1000 Threads

Question: Find derivative of f(x)=((x^2)(x^3))/((x^4)(x^2)) Attempt: ln f(x)=(lnx^2)+(lnx^3)-(lnx^4)-(lnx^2) Can someone tell me what I have done wrong so far? Thanks

Im having trouble solving these two questions. I don't know where to start so I can't give an attempt at either of them. Please tell me how to do the full question if you can cause i can't check back until morning then i have to go to an exam. http://www.users.on.net/~rohanlal/one.jpg...

(x^2-y^2)^2=(x+y)^3 I tried to use the chain rule on both sides but it didn't work because y needs to have the chain rule used on it explicitly and if i differentiate y explicitly then use the chain rule on everything i would be finding the 2nd derivative. So how do i differentiate this?

Homework Statement A curve has parametric equaions: x = 2cot t, y = 2sin²t, 0 < t <= pi/2 Find an expression for dy/dx in terms of the parameter t The Attempt at a Solution Not sure where to go. Do i need to make a Cartesian equation first? Thanks :)

[SOLVED] Differentiation of displacement and time to get velocity A moving body is related to a fixed point by the displacement equation: s = 12( 1 - e^-t). Assuming the body is moving in a straight line on a flat plain. 1. obtain an expression for the velocity after time t seconds. 2...

Hey there, this should be a very simple problem, but again, I haven't had much guidance in finding formulas with differentiation. If anyone could help me with this i'd greatly appreciate it as it can help me to understand the others. Characteristics of SHM are displacement (x) and time (t)...

Homework Statement x = 5sin(2y +6) find dy in terms of x Homework Equations The Attempt at a Solution dx/dy = 8 cos (2y+6) dy/dx = 1 / (8cos(2y+6) but according to the mark scheme the final answer is + or - 1 / (2 sqrt[16/x^2]) i don't see how on Earth they got...

Homework Statement Find \frac{dU_{ave}}{d\beta} where U_{ave}=\sum_{k}\left(\frac{U_{k}exp(-U_{k}\beta)}{exp(-U_{k}\beta)}\right) Homework Equations The Attempt at a Solution My answer is supposed to be -(U_{ave}^{2})+(U_{ave})^{2} However I keep getting zero. I can...

Homework Statement (x - h)^2 + (y - k)^2 = r^2 where h,k and r are constants The Attempt at a Solution \begin{array}{l} \frac{d}{{dx}}\left[ {(x - h)^2 + (y - k)^2 } \right] = \frac{d}{{dx}}r^2 \\ 2(x - h) + 2\frac{{dy}}{{dx}}(y - k) = 0 \\ \Rightarrow \frac{{dy}}{{dx}}...

Homework Statement Differentiate f = arctan(u/v) with respect to u The Attempt at a Solution Using the chain rule fu = (1/(1 + (u/v)2)) * 1/v = 1/(v + u2/v) The solutions manual says v/(u2 + v2) What is my mistake?

Homework Statement Prove that if f''(x) exists and is continuous in some neighborhood of a, than we can write f''(a)= \lim_{\substack{h\rightarrow 0}}\frac{f(a+h)- 2f(a)+f(a-h)}{h^2} The Attempt at a Solution I just proved in the first part of the question, not posted, that...

Solved: Real Analysis, differentiation Homework Statement If g is differentiable and g(x+y)=g(x)(g(y) find g(0) and show g'(x)=g'(0)g(x) The Attempt at a Solution I solved g(0)=1 and I got as far as g'(x)=\lim_{\substack{x\rightarrow 0}}g(x) \frac{g(h)-1}{h} but now I...

Homework Statement If dy/dx=xy^2 and x=1 when y=1, then y= (A) x^2 (B) -2/(x^2 -3) (C) x^2 + 3 (D) 2/(x^2 +1) (E) (x^2 -3)/2 Homework Equations The Attempt at a Solution dy/dx=xy^2 dy=xy^2dx dy/y^2=x dx ∫dy/y^2=∫x dx -1/y = x^2/2 + C y=-2/x^2 + C 1=-2/1^2 + C C=3...

helicopter moves vertically. Height above start point = y height at t seconds = y= (1/4)t^4 -26t^2 + 96t t = between 0 and 4 differentiate to find velocity = t^3 + 52t + 96 acceleration = 3t^2-52 thats part 1 of question done, easy.Verify that y has a stationary value when t =...

Homework Statement if g(t)=(10^t)(log...t) then evaluate g'(10) ......10 <---------(my attempt at a log base 10) Homework Equations im completely lost...i don't know if i should take the ln of both sides...or what to do really. The Attempt at a Solution

I need help differentiating this equation: y=(x-1)^2(6^x) What I have (I went wrong somewhere): dy/dx = (x-1)[(x-1)(6^x)] =(x-1)[6^x(1+ x ln6 - ln6) =(x-1)6^x(1+ x ln6 - ln6) So; My final answer: (x-1)6^x(1+ x ln6 - ln6) Answer in the textbook...

Differentiation ---Help, please! 1. Homework Statement 1) Use Newtons Method to approximate the real zero of the function f(x)=x^3 + 7x + 3 = 0 2) The curve y = x^3-2x^2+x-3 intersects the curve y = cos(2x). If x = 1.8 is used as the first estimate then, using Newton's Method, what is the...

We have implicit differentiation: i.e. x^2 + y^2 = 7 -> 2x +2y(dy/dx) = 0. and solve for dy/dx gives you the derivative of y with respect to x However, is there not implicit integration? for terms linear in y, i.e. x^2 + y = 7 -> X^3/3 +int(y) = 7x + K, and solve for int(y) to...

[URGENT] Differentiation of Geomertic Objects Homework Statement A sector of a circle has area 100cm². Show that the perimeter of this sector is given by te formula P = 2r + 200/r Homework Equations Area of sector = (angle/360) x pi x r^2 Permiter of sector = (angle/360) x 2 pi x r...

Help please on these. I'm extremely rusty with differentiation and want to know if I've got the right answers here Homework Statement differentiate the following functions (you do not have to simplify): a. f(x)=(x-2)^{3}e^{-2x} b. f(x) = cos x / ln (x^{2} + x) c. g(t) = cos^{4}(t^{2} +...

Implicit Differentiation of Cylinder NOT given radius? Homework Statement Question: Digging in his backyard, Dennis accidentally breaks a pipe attached to his water sprinkling system. water bubbles up at a rate of 1 cm^3/s, forming a circular pond of depth 0.5cm in his yard. How quickly is...

we are given some component of a vector potential A A = B\displaystyle\int^d_0 I(t')\,dt' where d = t -z/c and B = constant=1/2 mu0 (permeability constant) x c (speed of light) the derivation then wants me to calculate the magnetic field from this vector potential...

For those who don't know I'm writing a tutorial (https://www.physicsforums.com/showthread.php?t=139690") in the tutorials forum. I have come to the point of introducing Transcendental functions. I would like to introduce the exponential function first (via the Taylor series) and then present...

The question and my workings are attached:

f(x,y)=2e^(x^2y), then fx(0,1) = ? fx = 4xye^(x^2y) =4(0)(1)e^(0)(1) =e^0 =1? I'm told that I'm getting this question wrong but don't know how. Can anybody please help show me what I'm doing wrong on this one?

Homework Statement The potential energy of a system of two particles separated by a distance r is given by U(r) = (A)/(r^4), where A is a constant. Find the radial force that each particle exerts on the other. (Use A and r as appropriate in your equation.) Homework Equations F=-dU/dx U is...

Homework Statement 1) If f(x)= sin^4x, then f '(pi/3) 2) Given f(x) = x/tanx, find f '(3pi/4) 3) If f(x) = sinxcosx, then f '(pi/6) 4) Differentiate: f(x) = x^2 + 2tanx Question that I have answered but not sure if it's really the right answer: 5) Find the equation of the tangent line...

Homework Statement Supposed "f" is a differentiable function. Write the expression for the derivative of the following function. a) h(x) = -4x^3 * f(x) b) h(x) = 2/\sqrt{x}* f(x) Homework Equations N/a The Attempt at a Solution Would the answers just be (using the product...

simple SIMPLE local extremia question Homework Statement Find the absolute maximum and absolute minimum values of f(x) = 3x^4 - 8x ^3 + 12x^2 -48x +25, where 0 <= x <= 3. Homework Equations N/a The Attempt at a Solution f'(x) = 12x^3 - 24x^2 + 24x -48 = 12 (x^3 - 2x^2 +...

Hello,This is my first crack at using log differentiation, but I can't seem to get too far with it... Use logarithmic differentiation to calculate the derivative for the following function: y = \sqrt{x}e^{x^{2}} (x^{2} + 1)^{10} lny = \frac{1}{2}lnx * x^{2}lne * 10ln(x^{2} + 1)...

[SOLVED] Implicit Differentiation -4x^2+3xy+4y^3=-328 This is at the point (3,-4) and i am trying to find m Homework Equations The Attempt at a Solution here is my work -4x^2+3xy+4y^3=-328 -8x+3xy'+3y+12y^2y'=0 -8x+3y=-3xy'-12y^2y' -8x+3y=[-3x-12y^2]y'...

[SOLVED] Implicit Differentiation [b]-4x^2+3xy+4y^3=-328 This is at the point (1,3) Homework Equations The Attempt at a Solution here is my work -4x^2+3xy+4y^3=-328 -8x+3xy'+3y+12y^2y'=0 -8x+3y=-3xy'-12y^2y' -8x+3y=[-3x-12y^2]y' y'=(-8x+3y)/(-3x-12y^2) plug in x=1,y=3...

http://img442.imageshack.us/img442/6018/scoreqt9.jpg Can someone explain what this notation means regarding differentiating please. I've never seen it this way using the integration symbol, so I have no idea where to start. :) thx

Find y' = dy/dx for x3 + y3 = 4 Okay, now what's really confusing me is that for the y3 is that you need to use the chain rule for it. When you do, the answer is 3y2(dy/dx). How does that actually work? And if anyone can give me any good advice on any good guidelines on how to properly...

[SOLVED] differentiation of cos(x)cos(y) or sin(x)sin(y) Homework Statement Determine if the equation is exact, if exact solve. [cos(x)cos(y)+2x]dx-[sin(x)sin(y)+2y]=0 Homework Equations I have forgotten how to take the derivative of cos(x)cos(y) or sin(x)sin(y). Is this a product rule...

f(x,y)=e2x*ln(x/y^2) find f(subscript-x) Can anyone help me with this differentiation please? I know you must treat y as a constant and differentiate with respect to x.

Let f(x+iy)=u(x,y)+iv(x,y). Suppose we know |f|^2=u^2+v^2 is a constant function. Then we are allowed to say that (u^2+v^2)_x=(u^2+v^2)_y=0. But are we allowed to differentiate u by x and v by y? IE, are we allowed to make the following statement: (u^2)_x+(v^2)_y=0 I'm guessing 'no', but...

Question: For the graph x^2-8x+4 : (i) find the coordinates of the stationary point; (ii) say, with reasoning, weather this is a maximum or minimum point; (iii) check your answer by using the method of 'completing the square' to find the vertex; (iv) state the range of values which the...

okay, so i have the problem tan(xy)=xy and i am told to implicitly differentiate in terms of x and y. when i do, i keep getting an indefinite answer. i need help because i know that's not right.

Homework Statement how do i determine whether a function is bounded using differentiation eg: f(x)=x/(2^x) Homework Equations The Attempt at a Solution i know it has something to do with maximums and minimums but i can't figure out how to do it. any help would be appreciated...

Homework Statement Use implicit differentiation to show that the one parameter family f(x, y)=c satisfies the differential equation dy/dx = -f_{x}/f_{y} , where f_{x}=\frac{\partial f}{\partial x} and f_{y}=\frac{\partial f}{\partial y} .Homework EquationsThe Attempt at a Solution Well, my...

Given a tensor field T(x,y,z), how would I go about differentiating it wrt spatial coordinates? I would presume that it would work like this: \begin{equation} \frac{\partial T}{\partial x} = \lim_{h\to 0}\frac{T(x+h,y,z)-T(x,y,z)}{h} \end{equation} However, this does not seem to...

"the equation of a curve is x^2y=x-6 (x^2y is x squared times y) The normal of the curve at the point where x=-2 meets the x-axis at p. Find the coordinates of P" The method I used was to find y by rearranging the given equation and differentiate it. This gave me f ' (x)= 1+12x^-3...

Hi, I need some help with these question, and would appreciate the help. Homework Statement Part 1 Use implicit differentiation to find y'' if 2xy = y^2 Simplify and Leaev in terms of x and y. Part 2 Use implicit differentiation to find y '' if xy + y^3 = 1 Simplify your answer and...

I was just messing around on another problem I was trying to solve for someone in the homework forums when I stumbled on this: If we denote the n-th derivative the same way we do for exponents, eg the second derivative of f will be denoted by f^2, and the original function as its zero-th...

The contiunity equation is given as: ln(\rho) + ln(A) + ln(V)=constant "Differentiating Eq. 11.43 we get: \frac{d\rho}{\rho}+ \frac{dA}{A} +\frac{dV}{V}=0 My question is, what is this differentiated with resepct to? Its clearly not \rho, A or V alone.

Hey guys, I'm having trouble memorizing the the derivatives of the trig functions. I can memorize them for a while, but I eventually forget them all after one day. Does anyone know any sort of hooks or tricks that will make this process easier?

I'm having trouble with the following questions about differention with respect to x. Differentiate with respect to x: a) y= 2/ (2x+3)^4 b) y= x(x+1)^(1/2) c) y= (x +1)(x^2 + 3x)^3 d) y= 3x^3 + 3x^(-1/2) + 2 Any help would be greatful

Ok here goes... z=x^{2}+y^{2} x=rcos\vartheta y=r sin\vartheta Find: \[ \frac{\partial z}{\partial x}_{y}, \[ \frac{\partial z}{\partial \vartheta}_{x}, \[ \frac{\partial z}{\partial r}_{y}, \[ \frac{\partial z}{\partial r}_{ \vartheta}...

Homework Statement I have a differentiation operator on P_3, and: S = {p \in P_3 | p(0) = 0}. I have to show that 1) D maps P_3 onto the subspace P_2 2) D : P_3 -> P_2 is NOT one-to-one 3) D: S -> P_3 is one-to-one 4) D: S -> P_3 is NOT onto. The Attempt at a Solution...