\[\frac{d}{dx} \sin^{2}x\cos^{3}x\]

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Examples

Use Product Rule to find the derivative of

\sin^{2}x\cos^{3}x

. The product rule states that

(fg)'=f'g+fg'

(\frac{d}{dx} \sin^{2}x)\cos^{3}x+\sin^{2}x(\frac{d}{dx} \cos^{3}x)

Use Chain Rule on

\frac{d}{dx} \sin^{2}x

. Let

u=\sin{x}

. Use Power Rule:

\frac{d}{du} {u}^{n}=n{u}^{n-1}

2\sin{x}(\frac{d}{dx} \sin{x})\cos^{3}x+\sin^{2}x(\frac{d}{dx} \cos^{3}x)

Use Trigonometric Differentiation: the derivative of

\sin{x}

\cos{x}

2\sin{x}\cos^{4}x+\sin^{2}x(\frac{d}{dx} \cos^{3}x)

Use Chain Rule on

\frac{d}{dx} \cos^{3}x

. Let

u=\cos{x}

. Use Power Rule:

\frac{d}{du} {u}^{n}=n{u}^{n-1}

2\sin{x}\cos^{4}x+\sin^{2}x\times 3\cos^{2}x(\frac{d}{dx} \cos{x})

Use Trigonometric Differentiation: the derivative of

\cos{x}

-\sin{x}

2\sin{x}\cos^{4}x-3\sin^{3}x\cos^{2}x

Done

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