EhHannuh1458 EhHannuh1458

26-06-2020
Mathematics

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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 )equals 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 .

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LammettHash LammettHash

26-06-2020

By the chain rule,

[tex](f(g(x)))'=f'(g(x))g'(x)[/tex]

so that when [tex]x=1[/tex], we have

[tex](f(g(1)))'=f'(g(1))g'(1)=f'(9)g'(1)=6\cdot8=\boxed{48}[/tex]

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