differentiable functions f and g, such that... (composition)

[Math wiz ya rite 09]

Let f and g be differentiable function such that

f(1) = 4
g(1) = 3
f'(3) = -5
f'(1) = -4
g'(1) = -3
g'(3) = 2

If h(x) = f(g(x)), then h'(1) =

A. -9
B. 15
C. 0
D. -5
E. -12

 

[galactus]

Since \(\displaystyle \L\\h(x)=f(g(x))\)

Use the chain rule:

\(\displaystyle \L\\h'(x)=f'(g(x))\cdot{g'(x)}\), where x=1

 

[Math wiz ya rite 09]

do i have to plug in values now?

if so i get B. 15 for the answer


thanks!!!

 

[galactus]

That's right