Chris Cruz

2021-12-19

What is the derivative of ${\mathrm{sin}}^{2}\left(x\right)$

Hattie Schaeffer

Expert

Explanation
You would use the chain rule to solve this. To do that, youll

Bernard Lacey

Expert

$y={\mathrm{sin}}^{2}\left(x\right)$
First -method:-
$\frac{dy}{dx}=2\mathrm{sin}x\mathrm{cos}x=\mathrm{sin}2x$. Answer.
Second - method:-

$y=\frac{1.-\mathrm{cos}2x}{2}$
$y=\frac{1}{2}.-\frac{1}{2}\mathrm{cos}2x$S
$\frac{dy}{dx}=0-\frac{1}{2}.\left(-\mathrm{sin}2x\right).2$
$\frac{dy}{dx}=\mathrm{sin}2x.\text{Answer.}$

RizerMix

Expert

$y={\mathrm{sin}}^{2}x.$ Let $\mathrm{sin}x=t,dt/dx=\mathrm{cos}x$
So $y={t}^{2}.$ Diff. W.r.x.
$dy/dx=2t.dt/dx=>dy/dx=2\mathrm{sin}x\mathrm{cos}x$

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