How do you differentiate $f(x)=sin e^(4x)$ using the chain rule.?

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Answer 1 · 2015-12-03T12:29:40

$f'(x)=4e^(4x)cos(e^(4x))$

$f'(x)=color(red)(cos(e^(4x))color(blue)(d/dx[e^(4x)]$

$color(blue)(d/dx[e^(4x)])=e^(4x)d/dx[4x]=color(blue)(4e^(4x)$

$f'(x)=color(blue)(4e^(4x))color(red)(cos(e^(4x))$

Notice that the chain rule actually occurred twice.

How do you differentiate f(x)=sin e^(4x)f(x)=sin e^(4x) using the chain rule.?