Question

Write the derivative of sinx with respect to cos x ?

Answer 1

\[\text { Let u } = \sin x \text { and v} = \cos x\]
\[ \Rightarrow \frac{du}{dx} = \cos x \text { and }\frac{dv}{dx} = - \sin x\]
\[ \therefore \frac{\frac{du}{dx}}{\frac{dv}{dx}} = \frac{\cos x}{- \sin x}\]
\[ \Rightarrow \frac{du}{dv} = - \cot x\]