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

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Answer 1 · 2016-06-21T05:21:00

$e^cos(sqrt(x)) xx (-sin(sqrt(x))) xx 1/(2sqrt(x))$

Understand this that this is in the form of $f(g(h(x)))$ where $f(x) = e^x$ , $g(x)=cos(x)$ and $h(x) = sqrt(x)$

First, you need to know these things

$d/dx(e^x)=e^x$
$d/dx(cos(x))=-sin(x)$
$d/dx(sqrt(x))=1/(2sqrt(x))$

So, this becomes

Derivative = $e^cos(sqrt(x)) xx (-sin(sqrt(x))) xx 1/(2sqrt(x))$

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