Question

Differentiate \(cos (\sqrt x)\)with respect to x

1. \( \dfrac{-cos \sqrt x}{2\sqrt x }\)
2. \( \dfrac{sin \sqrt x}{2\sqrt x }\)
3. \( \dfrac{-sin \sqrt x}{2\sqrt x }\)
4. \( \dfrac{-sin \sqrt x}{\sqrt x }\)
5. \( \dfrac{sinx \ cosx \sqrt x}{2\sqrt x }\)

Answer 1

Correct Answer - Option 3 : \( \dfrac{-sin \sqrt x}{2\sqrt x }\)

 Let

\(y = cos (\sqrt x)\)

\(\dfrac{dy}{dx}= \dfrac{d}{dx}(cos \sqrt x)\)

\( \Rightarrow - sin \sqrt x \dfrac{d}{dx}(\sqrt x) \)

\(\Rightarrow \dfrac{-sin \sqrt x}{2\sqrt x }\)