Question

Calculate f'(-1)

f(x) = x^7 * h(x)
h(-1) = 5
h'(-1) = 8

Answer is 27, but I got no idea how to get there.

Answer 1

first, recall chain rule, since there there is a function of x multiplied by another function of x (that is, x^7 and h(x)),, given a function f(x)=g(x)*h(x)
f'(x) = g'(x)*h(x) + g(x)*h'(x)

therefore, to get derivative of f(x)=x^7 *h(x), first get the derivative of x^7 multiplied by h(x) plus the derivative of h(x) [which is h'(x)] multiplied by x^7,,

since it is evaluated at -1, substitute values for h(-1) and h'(-1), which is given in the problem,,

so there,, please ask questions if there's something you did not understand,, :)

Answer 2

find f' (x) first of all using the product rule assuming we are differentiating with respect to x

f' (x) = x^7 (h' (x)) + 7x^6 (h(x))

so f'-1) = (-1)^7 (h'(-1)) + 7(-1)^6 (h(-1))
= -1(5) + 7(-1)^6 (8)
=-5 + 56
= 51

I don't see how they got 27

Answer 3

I see my error, I substituted the wrong way, should have been ...

so f'-1) = (-1)^7 (h'(-1)) + 7(-1)^6 (h(-1))
= -1(8) + 7(-1)^6 (5)
= -8 + 35
= 27