Question

Differentiate sin²x w.r.t. x²

Answer 1

Let u = sin²x, v = x² 

Differentiate both w.r.t. x 

\(\frac{du}{dx}\) = 2 sin x. cos x, 

\(\frac{dv}{dx}\) = 2x

∴ \(\frac{du}{dv}\) = \(\frac{\frac{du}{dx}}{\frac{dv}{dx}} = \frac{2sinxcosx}{2x}\)

= \(\frac{sinxcosx}{x}\)