f(x)=x^6h(x) h(−1) = 5 h′(−1) = 8 f′(−1)=?

Question

Given that

f(x)=x^6h(x)

h(−1) = 5

h′(−1) = 8

f′(−1)=?

Answer 1

Answer 2

f(x) is the product of x⁶ and h(x) meaning that to find the derivative you must use the product rule:

(u•v)' = u'v + uv' or, applied to this problem:

f '(x) = (x⁶)'•h(x) + (x⁶)•h'(x)

f '(x) = 6x⁵•h(x) + x⁶•h'(x)

f '(-1) = 6(-1)⁵•h(-1) + (-1)⁶•h'(-1)

f '(-1) = 6(-1)•5 + 1•8 = -30 + 8 = -22

Answer 3

f(x)=x^6h(x)

f'(x)=6x⁵ h(x)+x⁶h'(x)

f'(-1)= 6(-1)⁵h(-1)+(-1)⁶h(-1)

=-6*5+1*8 = -30+8=-22.