Question

$\frac{d}{dx} \cos( \sqrt{x} )$

Solve this problem as soon as possible. Irrelevant answers will be reported.​

Answer 1

$\text{Let y = cos \sqrt{x} . We need to find derivative of y with respect to x .}\\\\ \\\text{i.e, y' = (cos \sqrt{x} )' }\\\\\\\frac{dy}{dx}=\frac{d(cos\sqrt{x}) }{dx}\\ \\\\\text{= - sin \sqrt{x} . \frac{d\sqrt{x} }{dx} }\\\\\\\Rightarrow\text{As , (cos x)' = - sinx }\\\\\\\text{= -sin \sqrt{x} . \frac{1}{2\sqrt{x} } }\\\\\\\Rightarrow\text{As , ( \sqrt{x} )' = \frac{1}{2\sqrt{x} } }\\\\\\\boxed{\begin{minipage}{2cm}\text{ = - \frac{sin\sqrt{x} }{2\sqrt{x} } }\end{minipage}}$