Given that f ( x ) = x^8h( x ) h ( − 1 ) = 2 h ' ( − 1 ) = 5 Calculate f ' ( − 1 )

Question

Please help ASAP. I've been trying for hours and can't seem to get this one.

Given that ⁸

Calculate 

A step by step explanation would be really helpful so I can learn to be better at this myself.

Answer 1

We need to employ product rule here, since f(x) is given as the product of two functions. This is a common question type, where one of the functions is given by an explicit rule (in this case, x⁸), while the other (h(x) here) we are just given values for (and for its derivative).

f^'(x) = 8x⁷·h(x) + x⁸·h^'(x)

f^'(-1) = -8·h(-1) + h^'(-1) = -16 + 5 = - 11