Question

Given that
f(x) = x^{7} h(x)
h(-1) = 5
h'(-1) = 8

What is f'( -1 )?
How would i find f'(-1)

Answer 1

f'(x) as derivative right?

Answer 2

\[f(x)=x^7h(x)~~\Rightarrow~~f'(x)=7x^6h(x)+x^7h'(x)\]
by the product rule.

Given that \(h(-1)=5\) and \(h'(-1)=8\), you have
\[f'(-1)=7(-1)^6h(-1)+(-1)^7h'(-1)\\
f'(-1)=-7(1)(5)+(-1)(8)\]