Let f and g be differentiable functions 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)= ?

Question

Let f and g be differentiable functions 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)= ?

anonymous · Answer

use the chain rule, that 
$$(f(g(x))'=f'(g(x))\times g'(x)$$ so 
$$(f(g(1))'=f'(g(1))\times g'(1)$$ substitute the numbers and see what you get

anonymous · Answer

Is it (-4)(3) * (2)? Equalling -24?

anonymous · Answer

no

anonymous · Answer

it is not a product in the first part ,
it is 
$$f'(g(1))$$

anonymous · Answer

$$g(1)=3, f'(g(1))=f'(3)=-5$$ so it is 
\[f'(g(1))\times g'(1)=-5\times (-3)

anonymous · Answer

$$f'(g(1))\times g'(1)=-5\times (-3)$$

anonymous · Answer

OH okay. That makes sense then with why they give you f′(3). Thank you.

anonymous · Answer

they gave you lots of extra information to see if you knew what to do