Derivatives jsfuyvwbuyro

Question

Given that g(5) = −6,

 g′(5) = 5,

 h(5) = 6,

 and h′(5) = −2,

 find f ′(5)

 for each of the following, if possible. (If it is not possible, enter NOT POSSIBLE.)

(a)

f(x) = g(x)h(x)

f ′(5) = 

 

(b)

f(x) = g(h(x))

f ′(5) = 

 

 

(c)f(x)=g(x)/h(x)

f'(5)=

 

(d)

f(x) = [g(x)]³

f′(5) =

Answer 1

All you need here is write out the appropriate rule (product rule, chain rule, quotient rule in terms of g and h functions) and then put the function values for g(x) and h(x).

The tricky part is the place where you substitute for the composite functions

Note g(h'(x)) = g(h'(5) = g(-2) which you do not have information for.

h(g'(x)=h(g'(5)= h(5)=6