13 Answered Questions for the topic Product rule

Derivatives and the Product Rule

y=x^3 ln x + (e^2x +cos^2 x)^4


Compute f'(x) in three different ways

f(x)=(2x^2-5)^21.) multiplying out and then differentiating2.) Using the product rule3.) Using the chain ruleShow that the results coincide
Product Rule Calculus Derivative


Use product rule to calculate derivative



Calculate the Derivative in Two Ways

First use the Product or Quotient Rule. Then rewrite the function algebraically and directly calculate the derivative.h(t)= (t^2-1)/(t-1)
Product Rule Math Differentiation



y= -x5(1 - x)   I have to use the product rule to answer this question.    The answer is 6x5 - 5x4   Can someone explain this to me and show how to solve it?   Thank you so much!
Product Rule


Product Rule

Have been learning about product rule and stuck on this question:   The displacement, y(m), of a body in damped oscillation is y = 2e-tsin3t   Use the product rule to find an equation for... more


f(x) = 3√ x · sin x use the definition of derivative to show f(x) is differentiable at x=0

this question had several parts  1)Why can't we use the product rule to compute f'(0)    My initial thought was that you cannot use the product rule t because sinx and 3√ x both equal 0 at... more

I need help finding the derivative for this problem using the product rule

Product Rule


Derivative of h(x)=sqr(x) * (x^3+2x^2)..product rule

Hi, I keep getting wrong because Im not sure how to solve when it involves a radical.    h(x)=(√x)* (x3+2x2)   The only radical is the x and its being multiplied by the bracket. 


Using chain rule and product/quotient rule, find derivative of sin(3x^2)/x when x=(squareroot of pi)

sin(3x^2)x^-1   this is how far I got.  when do I sub in √pi ? what do I do next?
Product Rule The Product Rule


using product rule let y=uv

a)  (x2+1)3(x3+1)2    b)   (x2-1)√(1+x)      c)   (√1/x-x2)(x2+x)7
Product Rule Product


what is the product. ( x-9)(x+8)

Find  the product. (X-9)(x+8)

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