Differentiation Definition and 1000 Threads

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...

"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...

Homework Statement A car, traveling at a speed of 90km/h, approaches a stop sign 40m ahead. If the car immediately begins to decelerate at a rate of -8m/s^2, will it be able to stop in time? Justify your response Homework Equations d = 1/2at^2 + vt The Attempt at a Solution I...

Power of an electrical circuit is equal to current squared times resistance. My expression for current is: E/(R + r), where E is emf of battery. So, my expression for Power, P, is: P=((E^2)R)/(R + r)^2 I would like to differentiate P with respect to R, to find where the slope is...

Homework Statement I have nearly finished a problem. I am at the stage where I have: B(s)\propto\frac{1}{s^{3}} v=\frac{ds}{dt} I want to find the rate of change of B(s), but expressed in terms of a velocity, rather than a displacement. Homework Equations So for displacement: B'(s)...

What am I missing here Problem Statement: Let f be a differentiable at point x and assume f(x) is not equal to 0. Show that function 1/f is differentiable at x=0 and (1/f)' = -f'(x)/( f(x) ^2 ) Solution 1/f = f^-1. So taking its derivative I get the following: -f^-2. But I fail to...

Homework Statement f(\alpha) = \int \log(1+ \alpha \cos(x))dx I am supposed to differentiate w.r.t alpha and then integrate to find f(alpha). My book says that there should be a factor of pi in the answer but I do not get one. Does anyone else?Homework Equations The Attempt at a Solution

[SOLVED] Basic Differentiation Hi there, I've heard that this forum is the best for getting some quick help. Find the gradient of the tangent to the curve at the given point: y = 2x² + 3x + 5 when x = -1 Homework Equations Right, I'm very new a this, but dy/dx is the way to go right...

Problem statement Show that if F:(a,b)->R is differentiable at every point of (a,b) and increasing then f'(x) >= 0 for all x belonging to (a,b) Problem Solution Definition of differentiation: Assume sequence {an} -> a then f(an) - f(x) / (an -x) converges to some value Using this...

Homework Statement A curve has an equation .. y=x^3-5x^2+5x+2 a) find dy/dx in terms of x The points P and Q lie on C. The gradient of C at both P and Q is 2. The x-coordinate of P is 3 b) Fine the x-coordinate of Q c) Find and equation for the tangent to c at P, giving your...

please explain in more detail on how we come up with the answers below. Thanks in advance! (formulas much appreciated) Differentiate: 1. y=e^x =e^x 2. y=lnx =1/x

Homework Statement Obtain the derivative of e^{2x} from first principles. Homework Equations The Attempt at a Solution I am upto the point where i have e^{2x}(\frac{e^{2h}-1}{h}) Where LIM h->0. I just don't see how 2 is obtained from what's in the ().

Homework Statement "A lawn sprinkler is constructed in such a way that d\theta/dt is constant, where theta ranges between 45 degrees and 135 degrees. The distance the water travels horizontally is x=v^2sin(2\theta)/32 where v is the speed of the water. Find dx/dt and explain why this lawn...

using logarithmic differentiation I can get it to a point where I have... ln(y)=20[ln(x+sqrt(x))-ln(x^2-2^x)] I do not know what to do at that point

This isn't a homework problem but something that stumped me in selfstudy, however i see this to be the most approperiate place to ask for help nevertheless. This is straight out of Adan's calculus 6e, Chain rule section. y= (x^5)sqrt(3+x^6) / (4+x^2)^3 To me it looks like a...

Homework Statement An object with mass m moves along the x axis. It's position as a function of time is given by X(t)= At- Bt^2 + Ct^3 A,B,C are constants a) find expression for the net force acting on the object as a function of time. b) let A= 2m/s, B= 10m/s^2, and C= 1m/s^3...

1.Use implicit differentiation to find the equation of the tangent line to the curve xy^3+xy=16 at the point (8,1) . The equation of this tangent line can be written in the form y=mx+b 2.For the equation given below, evaluate y^1 at the point(1,-1) . (6x-y)^4+2y^3=2399. 3.Find the...

Homework Statement Find the slope of the tangent line to x tan y = y - 1 when y = pi/4 Homework Equations The Attempt at a Solution I can't seem to get the derivative. Here's what I do. First I used the product rule the left side of the equation and got sec^2 x dy/dx + tan...

Homework Statement Find d^2y/dx^2 in terms of x and y. x^2y^2-2x=3 Homework Equations property rule, chain rule, quotient rule, The Attempt at a Solution I can do this the long way, but there must be a shorter solution. Can I simplify it? I've found dy/dx=(-xy^2 +2x)/(2x^2y)...

Homework Statement A curve has equation y = Ax^3 + Bx^2 + Cx + D, where A, B, C and D are constants. Given that the curve has gradient -4 at the point (1,2) and gradient 8 at the point (-1,6), find A, B, C and D. Homework Equations The Attempt at a Solution y = Ax^3 + Bx^2 + Cx + D dy/dx =...