How do you differentiate $y = 3 x {cos}^{2} (x)$ $y = 3x cos^2 (x)$ ?

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How do you differentiate $y = 3 x {cos}^{2} (x)$ $y = 3x cos^2 (x)$ ?

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Answer 1 · 2018-02-01T22:58:07

$3 cos x$ $3cosx$ [ $cos x - 2 x sin x$ $cosx-2xsinx$ ]

Explanation:

$d$ $d$ [ $u v$ $uv$ ]= $v d u + u d v$ $vdu+udv$ this is the product rule, where v and u are both functions of x.

Let u = $3 x$ $3x$ and $v = {cos}^{2} x$ $v=cos^2x$

so we have ...... ${cos}^{2} x$ $cos^2x$ .[ $3]$ $3]$ + $3 x$ $3x$ [ $- 2 sin x cos x$ $-2sinxcosx$ ]

= $3 {cos}^{2} x$ $3cos^2x$ - $6 x sin x cos x$ $6xsinxcosx$ .....= $3 cos x [cos x - 2 x sin x$ $3cosx[cosx-2xsinx$ ].

${cos}^{2} x$ $cos^2x$ = ${[cos x]}^{2}$ $[cosx]^2$ and so need to use the chain rule to differentiate this, = $2 cos x$ $2cosx$ , times the derivative of $cos x$ $cosx$ which is - $sin x$ $sinx$ , so $\frac{d}{d x} {cos}^{2} x$ $d/dxcos^2x$ $= - 2 sin x cos x$ $=-2sinxcosx$ . hope this helped.

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How do you differentiate $y = 3 x {cos}^{2} (x)$ $y = 3x cos^2 (x)$ ?

1 Answer

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Science

Math

Humanities

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How do you differentiate y=3xcos2(x)y = 3x cos^2 (x)?

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Explanation:

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Impact of this question

How do you differentiate $y = 3 x {cos}^{2} (x)$ $y = 3x cos^2 (x)$ ?