How do you find the derivative of ${sin}^{2} x^{2}$ $sin^2x^2$ ?

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How do you find the derivative of ${sin}^{2} x^{2}$ $sin^2x^2$ ?

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Answer 1 · 2016-01-10T16:10:53

$4 x {sin x}^{2} {cos x}^{2}$ $4xsinx^2cosx^2$

Explanation:

before starting note that ${sin}^{2} (x) = {(sin x)}^{2}$ $sin^2(x) = (sinx)^2$

this form makes it'easier' to apply the chain rule.

rewriting ${sin}^{2} x^{2} = {({sin x}^{2})}^{2}$ $sin^2x^2 = (sinx^2)^2$

differentiating using the chain rule gives:

$2 ({sin x}^{2}) . \frac{d}{d x} ({sin x}^{2}) = 2 ({sin x}^{2}) ({cos x}^{2}) . \frac{d}{d x} (x^{2})$ $2(sinx^2).d/dx(sinx^2) = 2(sinx^2)(cosx^2).d/dx(x^2)$

$= 2 ({sin x}^{2}) {cos x}^{2} (2 x)$ $= 2(sinx^2)cosx^2(2x)$

$\Rightarrow \frac{d}{d x} ({sin}^{2} x^{2}) = 4 x {sin x}^{2} {cos x}^{2}$ $rArr d/dx(sin^2x^2 ) = 4xsinx^2cosx^2$

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How do you find the derivative of ${sin}^{2} x^{2}$ $sin^2x^2$ ?

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Explanation:

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