If f(x) and g(x) are differentiable functions such that f (1 )equals 4, f prime (1 )equals 5, f prime (9 )equals 6, g (1 )e

Question

2 years ago

13

If f(x) and g(x) are differentiable functions such that f (1 )equals 4, f prime (1 )equals 5, f prime (9 )equals 6, g (1 )e

quals 9, g prime (1 )equals 8, g prime (2 )equals 9, g prime (5 )equals 10, find StartFraction d Over dx EndFraction f (g (x ))vertical line Subscript x equals 1 Superscript .

Mathematics

1 answer:

Alex777 [14] · Answer 1 · 2022-03-27T13:10:52+03:00

Alex777 [14]2 years ago

8 0

By the chain rule,

$(f(g(x)))'=f'(g(x))g'(x)$

so that when $x=1$ , we have

$(f(g(1)))'=f'(g(1))g'(1)=f'(9)g'(1)=6\cdot8=\boxed{48}$

If​ f(x) and​ g(x) are differentiable functions such that f (1 )equals 4​, f prime (1 )equals 5​, f prime (9 )equals 6​, g (1 )e

If f(x) and g(x) are differentiable functions such that f (1 )equals 4, f prime (1 )equals 5, f prime (9 )equals 6, g (1 )e