given that f(x)=

Question

given that f(x)=x7h(x)f(x)=x7h(x)

h(−1)=5h(-1)=5

h'(−1)=8h′(-1)=8

Calculate f'(−1)f′(-1).

Answer 1

If f(x) = x⁷h(x), then, by the product rule, f'(x) = 7x⁶h(x) + x⁷h'(x)

So f'(-1) = 7(-1)⁶h(-1) + (-1)⁷h'(-1) = 7(5) - 8 = 27