What is the derivative of $f (x) = cos \sqrt{x}$ $f(x)=cossqrt(x)$ ?

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Answer 1 · 2015-12-12T12:31:31

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

Applying the chain rule, together with the derivatives

we get

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

$= - sin (\sqrt{x}) (\frac{1}{2 \sqrt{x}})$ $= -sin(sqrt(x))(1/(2sqrt(x)))$

$= - \frac{sin (\sqrt{x})}{2 \sqrt{x}}$ $= -sin(sqrt(x))/(2sqrt(x))$

What is the derivative of f(x)=cos√xf(x)=cossqrt(x)?