Product rule Definition and 138 Threads

This is NOT homework... If one takes the formula for work, which is force times distance, one can get the formula for power by taking the derivative of it with respect to time. But if we really do this correctly (by using calculus), we get: power=distance*(change of force/change in...

Homework Statement I was just wondering if there is a formula for the product rule when you take two derivatives ... ? Homework Equations I know the product rule for one derivative .. is u'v + uv' ! The Attempt at a Solution I just want a formula without a proof

Homework Statement Find the derivative of the function: f(x) = x^2((x-2)^4) Homework Equations f`(x) = (u)(y`) + (u`)(y) The Attempt at a Solution Via the product rule I got [x^2(4(x-2)^3)] + [(2x)(x-2)^4] the book then goes on to give the solution as 2x(x-3)^3 * (3x-2) I'm...

Homework Statement As part of a first order differential equation I need to find \frac{d}{dt}(mv) where v=\frac{dy}{dt} Homework Equations Product Rule. The Attempt at a Solution \frac{d}{dt}(m\frac{dy}{dt}) = m*\frac{d}{dt}\frac{dy}{dt} + \frac{dm}{dt}\frac{dy}{dt} = ?? I...

Homework Statement The points A and B have position vectors a = (2,2,1) and b (1,1,-4) respectively relative to an origin O. (im using column notation for shorthand) Prove that OA is perpendicular to AB Homework Equations The Attempt at a Solution To be perpendicular the...

Curl Product Rule confusion? Homework Statement In Griffith's Introduction to Electrodynamics, he gives the rule: \nabla\times(\bold{A}\times\bold{B})=(\bold{B}\cdot\nabla)\bold{A}-(\bold{A}\cdot\nabla)\bold{B}+\bold{A}(\nabla\cdot\bold{B})-\bold{B}(\nabla\cdot\bold{A}) Now I know I am...

Can someone please explain it to me? My handwriting wasn't at its best when I was taking notes in class and now I can't read it. The teacher showed an example that I jotted down but what's the general rule?

y=-1/2 x cosx y'=1/2 x sinx + cos x -1/2 y"= 1/2 x cosx - sin x 1/2 + cos x + -1/2 - sin x y"= 1/2 x cos^2x I used the product rule (fg)'=fg'+gf'

Determine a quadratic funtion f(x) = ax^2 + bx + c who graph passes through the point (2,19) and that has a horizontal tangent at (-1,-8). My attempt at this solution is: f(x) = ax^2 + bx + c f'(x) = 2ax + b LOL its not much but i really have absolutely no idea where to go from here :S

y = ( 5 x-2 ) 3 / ( 2 x+5 ) 4 I do it this way: f(x) = (5x-2)3 g(x) = (2x+5)-4 f'(x) = 3(5x-2)2 g'(x) = -4(2x+5)-5 By using the product rule: [3(5x-2)2](2x+5)-4 + (5x-2)3[-4(2x+5)-5] 3(5x-2)2(2x+5)-4 -4(2x+5)-5(5x-2)3 What's wrong with this answer?

Homework Statement (2x^2 - 3x + 1)(4x^3 + 4x -3)^5 Homework Equations The Attempt at a Solution

Hi 2 questions having a mental block and can't figure them out any help would be apprieciated Q1 differentiate f(x)=ax(2x+b)^7 where a and b are constants Q2 differentiate f(x)=(x^2+cos^3(x^4))^10 thanks for any help cheers

Hello everyone. I'm trying to get my head around this product rule: \nabla \times (A\times B) = (B\cdot \nabla )A - (A\cdot \nabla )B + A(\nabla \cdot B) - B(\nabla \cdot A) Ok, we have this \nabla = (\partial /\partial x,\partial/\partial y,\partial /\partial z) and for dot...

Homework Statement Differentiate y = u * e^t + v * t * e^t Homework Equations Product Rule. The Attempt at a Solution y = u' * e^t + u * e^t + ( v' * t * e^t + v * e^t + v * t * e^t) u and v are functions of t. I forgot whether the product rule works like this: d/dt [xyz] =...

I have a question more than a problem to answer. I'm having a difficult time recognizing when to use the product rule and when to use the chain rule. How do you recognize when to use each, especially when you have to use both in the same problem. Problems like y+x^4y^3-5x^6+3y^8-42=0 tend...

Homework Statement a) How many bit strings are there of length 8? b) How many bit strings are there of length 8 which begins with 2 1's? Homework Equations Product Rule The Attempt at a Solution a) Since a bit string is either 0 or 1 there are two possibilities for each one...

Homework Statement If f(x) = (3 x )(sin x) (cos x), find f'( x ). A question I have is , is there anything special to do when you have 3 products instead of 2 The Attempt at a Solution Well I used the product rule as if am multipling (3xsinx) (cosx) but that doesn't...

I ve been trying to derive this for some time now. The rule is similar to the one for simple math derivatives. d/dx(A^B^)=dA^/dx B^ + A^ dB^/dx Is the derivation on similar lines. Any directions??

Homework Statement y=2x(1-x)^2 Homework Equations The Attempt at a Solution y=2x(1-x)^2 y`=-x ----------------- (1-x)^1/2 I thought i was done here. The book takes a few more steps. it adds: -x ----------------- (1-x)^1/2 to this: 2(1-x)^1/2...

I've already done the problem (here is the last part, sorry for crappy pic) My question; if I multiply both sides of the + by x^2(x+1) / x^2(x+1) as the common factor to simplify the equation, then why does on of the x^2(x+1) disappear from the numerator in the final answer? It appears as...

We covered the product rule in maths last lecture, and as part of the derivation of it, we got this line: \frac{\partial y}{\partial x}=\frac{u \partial v}{\partial x} + \frac{v \partial u}{\partial x} + \frac{\partial u \partial v}{\partial x} And were told that as x \rightarrow 0...

im having a lot of trouble using the chain rule product rule and quotient rule..i can do them fine seperatly but when they're put together i can't get them like if you have (x^2-1)^4 (2-3x) i would start with 4(x^2-1)^3(2x)(2-3x)+(x^2-1)^4(-3) have i done something wrong here because i never...

If f(8) = 7, g(8) = 5, f '(8) = -4, and g '(8) = 6, find the following numbers. (a) Find (f + g)'(8). i was tryig to apply the product rule to this by doing (f+g)(8)'+(f+g)'(8)...so 0+(f+g)'(8)...so that would be (-4+6)8...but that is not the right way to do it... please help me...

Hi, I'm having trouble following the following derivation I have seen in a textbook: The derivation goes as follows: L0P3+L1P2+L2P1=0 This is a Poisson eqn for P3 with respect to L0 which requires <L1P2+L2P1>=0 <L2>=L(BS)(sigma) <L1P2>=.5<L1.phi(y)>.x^2. d^2P0/dx^2 thus...

Homework Statement Use the product rule to show that dx^n-1/dx = (n-1)x^n-2 Homework Equations The general idea is.. If: h(x) = f(x)g(x) Then: dh(x)/dx = f(x)dg(x)/dx + g(x)df(x)/d(x) The Attempt at a Solution It seems like a simple solution but everytime I attempt solving it...

hey, ive been given a problem where vector a = 2i + 3j and vector b = \lambdai + 12j and also told that these vectors are parallel of each other. i understand since the vectors are parallel of each other, the angle between them would be equal to zero, thus i could apply the scalar product rule...

It's been too long since I've had an algebra class, so I start getting into trouble as these calculus questions rely more and more on algebra. \begin{array}{l} y = (4x - 5)^4 \,(3x + 1)^5 \\ {\rm{Find the first derivative}}{\rm{. Simplify if possible (i}}{\rm{.e}}{\rm{...

Say for example, to differentiate x/(x²+1) I would use to quotient rule. However, would it be legal to bring up the denominator to: (x)(x²+1)-¹ and use the product/chain rule instead?

hey there, At the moment at school I'm doing Implicit Differentiation. If i had for Instence 2y'yx + 6x = 0 how can I use the product rule on the first step when there are 3 variables? Cheers- Andy

How do I carry out the product rule for xy'z' Is it possible to do the product rule with y'z' and after that multiply it by x?

A problem which I'm sure is rather simple, however I cannot seem to simplify the equation properly to produce the fully simplified answer as written in my textbook. The problem being. f(x)= e^{4x}{(1-2x)}^4 Find f ' (X) All help is greately appreciated!

\int x sin (2x) dx =? u=2x du=2dx \int \frac{u}{2} sin(u) \frac{du}{2} \frac{1}{4} \int usin(u)du \frac{1}{4} (\frac{u^2}{2}sin(u)+u(-cos(u))) \frac{2x^2}{4} sin(2x)-\frac{1}{2} cos(2x)+C is this correct?

y = x ln x \frac{dy}{dx} = \frac{1}{x ln x} \cdot 1 Is that correct?

(2x+3)^3(x-4) How do I differentiate this?

Hi all! I've been working with differentiation for quite some time now, and I know how to use the product rule. f(x) = u(x)*t(x) f'(x) = u'(x)*t(x) + t'(x)u(x) But what I don't understand is how one derives it... :cry: Oh, and one more thing. How do we know a number is irrational...

Hey what's up, The problem is...find the derivative of: y= x^2 sec(x-5) My question is...Would I start off by using the product rule and combine the chain rule with it, with x-5 being the inner function and sec(u) being the outer function? thanks...

Here's the equation: F(x) = (x-1)(x-2)(x-3) I know how to diff. using the product rule when you only have 2 equations, but not 3.I looked at the examples in my book and none of them show how you would work out this sort of problem. So if someone could give me the basic overview of how to...

Can the product rule be applied if one of the functions is not differentiable? For example, f(x)={g(x)sin(1/x), x not =0 =0, x=0 where g(0)=g'(0)=0. f'(0)=g'(0)sin(1/0) + g(0)dsin(1/x)/dx =0sin1/0+0dsin(1/x)/dx=0? applying the limit definition, I get f'(0)=g'(0)lim sin(1/h) where...