Let f and g be differentiable functions such that f (1) = 2, f' (1) = 3, f' (2) = - 4, g (1) = 2, g' (1) = - 3, g' (2) = 5. If h (x) = f (g (x)), then h' (1) =

Question

Mathematics

Natalya

8 August, 17:11

Let f and g be differentiable functions such that f (1) = 2, f' (1) = 3, f' (2) = - 4, g (1) = 2, g' (1) = - 3, g' (2) = 5. If h (x) = f (g (x)), then h' (1) =

+4

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Shannon Barnett · Answer 1

12

Step-by-step explanation:

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

Using chain rule:

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

h' (1) = f' (g (1)) g' (1)

h' (1) = f' (2) g' (1)

h' (1) = - 4 * - 3

h' (1) = 12