Question

Given that
f(x) = x^8 h(x)
h(-1) = 4
h'(-1) = 7

Calculate f'(-1) using the product rule and the power rule. How do I do that? Can you please show and explain? Thank you.

Answer 1

\(f'(x)=8x^7~h(x)+x^8~h'(x)\)

So \[\begin{array}~f'(-1)&=8(-1)^7~h(-1)+(-1)^8~h'(-1)\\~\\&=-8(4)+7\\~\\&=\boxed{-25}\end{array}\]

Answer 2

Thank you so much.