Question

Find the derivative of sin x² with respect to x³.

Answer 1

Let u = sin x² and v = x³.

we have to find du/dv

du/dx = cos x² . 2x = 2x cos x² , dv/dx = 3x²

\(\therefore \,\frac{du}{dv}=\frac{du}{dx}/\frac{dv}{dx}=\frac{2x\,cos\,x^2}{3x^2}=\frac{2\,cos\,x^2}{3x}\)