Home > Calculus > Product Rule

How do you differentiate #f(x) =(x^2+1)(x-3)^3# using the product rule?

Answer 1

Ezra Adams

#f'(x)=3(x^2+1)(x-3)+6x(x-3)^2#

The product rule sates that #d/dx[f(x)*g(x)]=f(x)*g'(x)+g(x)*f'(x)#

Consequently, in the example provided, we require the power rule for the second factor, and obtain

#f'(x)=(x^2+1)*3(x-3)+3(x-3)^2*2x#

By signing up, you agree to our Terms of Service and Privacy Policy

Answer 2

Aurora Alvarado

To differentiate the function ( f(x) = (x^2 + 1)(x - 3)^3 ) using the product rule, you would apply the formula ( (uv)' = u'v + uv' ), where ( u = x^2 + 1 ) and ( v = (x - 3)^3 ). Then differentiate ( u ) and ( v ) separately and apply the product rule.

By signing up, you agree to our Terms of Service and Privacy Policy

Answer from HIX Tutor

When evaluating a one-sided limit, you need to be careful when a quantity is approaching zero since its sign is different depending on which way it is approaching zero from. Let us look at some examples.