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Let $y= (\sin x)^{2}$ then dy/dx equals

Option 1)
$(\cos x)^{2}$

Option 2)
$2\sin x \cos x$

Option 3)
$2\sin x$

Option 4)
none of these

Answers (1)

best_answer

As we have learned

Chain Rule for differentiation (indirect) -

Let y = f(x) is not in standard form then

$\frac{dy}{dx}=\frac{dy}{du}\times \frac{du}{dx}$

$ex:\:\:y=sin(ax+b)$

$Let\:\;u=(ax+b)$

$then\:\:y=sin \:u$

$so\:\:\frac{dy}{du}=cos \:u\:\:and\:\:\frac{du}{dx}=a$

$\therefore \frac{dy}{dx}=\frac{dy}{du}\times \frac{du}{dx}=a\:cos \:u$

$=a\:cos(ax+b)$

- wherein

$Where\;\:y=f(u)\:\;and\;\;u=f(x)$

$\frac{dy}{dx}=\frac{dy}{dx}*\frac{du}{dx}$ , Let $u= \sin x\Rightarrow \frac{du}{dx}=\cos x$ and also

$y=u^{2}\Rightarrow \frac{dy}{dx}=2u$

$\therefore \frac{dy}{dx} = 2u*\cos x= 2\sin x \cos x$

Option 1)

$(\cos x)^{2}$

Option 2)

$2\sin x \cos x$

Option 3)

$2\sin x$

Option 4)

none of these

Posted by

Himanshu

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