Question

Differentiate of sin²x is equal to

Answer 1

2 sinx.cosx= sin2x
........

Answer 2

Answer:

$\red { \frac{d}{dx}(sin^{2}x) }\green { =2sinxcosx}$

Step-by-step explanation:

$Let \: y = sin^{2} x$

$put \: v = sin \: x\:---(1) ,\: we \: get$

$y = v^{2} \: ---(2)$

$Differentiate \: equation \:(1) , with \: respect \\to \: v , \:we \:get$

$\implies \frac{dv}{dx} = cos\:x \: ---(3)$

$Differentiate \: equation \:(2) , with \: respect \\to \: v , \:we \:get$

$\frac{dy}{dv} = 2v \: ---(4)$

/* From (3) and (4) , we get

$\frac{dv}{dx} \times \frac{dy}{dv} = cosx \times 2v \\= cosx \times 2sinx\\= 2sinxcosx$

Therefore.,

$\red { \frac{d}{dx}(sin^{2}x) }\green {=2sinxcosx}$

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