Question

differentiate y=sin²x​

Answer 1

I think it helps you

Answer 2

Correct Question :-)

Differentiate funtion

y=sin²x

With respect to x

FORMULAS USED

$1) \: \: \: \:\dfrac{d}{dx} [ f(x)] {}^{n} = n[f(x)] {}^{n - 1} .\dfrac{d}{dx}f(x) \\ \\ 2) \: \: \: \:\dfrac{d}{dx}sin \: x \: = \: cos \: x \\ \\ 3) \: \: \: \: 2 \sin(x) \cos(x) = \sin(2x)$

Solution :-)

Given Function is

$y = {sin}^{2} x$

Now Differentiating Both side w.r.t. x

$\dfrac{dy}{dx} = \dfrac{d}{dx} ( {sin}^{2} x) \\ \\ = 2sin \: x.\dfrac{d}{dx}sin \: x \\ \\ = 2sin \: x.(cos \: x) \\ \\ = 2sin (x ) cos(x) \\ \\ = \sin2x$

So

$\green{ \boxed{ \boxed{{{\dfrac{dy}{dx}=Sin2x}}}}}$