Differentiate sin2x w.r.t. x2

1.	Differentiate sin2x w.r.t. x2
Answer» Let u = sin²x, v = x² Differentiate both w.r.t. x \(\frac{du}{dx}\) = 2 sin x. cos x, \(\frac{dv}{dx}\) = 2x ∴ \(\frac{du}{dv}\) = \(\frac{\frac{du}{dx}}{\frac{dv}{dx}} = \frac{2sinxcosx}{2x}\) = \(\frac{sinxcosx}{x}\)

Answer»

Let u = sin²x, v = x²

Differentiate both w.r.t. x

\(\frac{du}{dx}\) = 2 sin x. cos x,

\(\frac{dv}{dx}\) = 2x

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

= \(\frac{sinxcosx}{x}\)

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