Suppose h = f∘g. Find h'(0)

Question

Given that

f(0) = 5

f '(5) = -7

g(0) = 5

g '(0) = 4

 

Answer 1

Thank you for the clarification.  If

 

h(x) = f(g(x)),

 

then use the chain rule to get h'(x).

 

h'(x) = f'(g(x)) g'(x)

 

h'(0) = f'(g(0)) g'(0)

 

g(0) = 5

g'(0) = 4

f'(5) = -7

 

h'(0) = [f'(5)] (4) = (-7)(4) = -28

Answer 2

Given that the values are f(0)=0, f'(5)=-7,g(0)=5,g'(0)=4.

To find the value of h'(0).

Use chain rule formula to find the value of h'(0).

The chain rule formula is as follows.

h'(x)=f'(g(x)).g'(x)

Substitute x=0 in the above formula is as follows.

h'(0)=f'(g(0)).g'(0)

h'(0)=f'(5).(4)

h'(0)=-7×4=-28

Hence the value of h'(0)=-28.