How do you differentiate $f (x) = e^{cos \sqrt{x}}$ $f(x)=e^(cossqrtx)$ using the chain rule.?

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How do you differentiate $f (x) = e^{cos \sqrt{x}}$ $f(x)=e^(cossqrtx)$ using the chain rule.?

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Answer 1 · 2016-06-21T05:21:00

$e^{cos (\sqrt{x})} \times (- sin (\sqrt{x})) \times \frac{1}{2 \sqrt{x}}$ $e^cos(sqrt(x)) xx (-sin(sqrt(x))) xx 1/(2sqrt(x))$

Explanation:

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

First, you need to know these things

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

So, this becomes

Derivative = $e^{cos (\sqrt{x})} \times (- sin (\sqrt{x})) \times \frac{1}{2 \sqrt{x}}$ $e^cos(sqrt(x)) xx (-sin(sqrt(x))) xx 1/(2sqrt(x))$

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How do you differentiate $f (x) = e^{cos \sqrt{x}}$ $f(x)=e^(cossqrtx)$ using the chain rule.?

1 Answer

Explanation:

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How do you differentiate $f (x) = e^{cos \sqrt{x}}$ $f(x)=e^(cossqrtx)$ using the chain rule.?