Explained: "What is the derivative of sin2(x)"

Chris Cruz

Answered question

2021-12-19

What is the derivative of

\sin^{2} (x)

Hattie Schaeffer

Beginner2021-12-20Added 37 answers

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

Bernard Lacey

Beginner2021-12-21Added 30 answers

y = \sin^{2} (x)

First -method:-

\frac{d y}{d x} = 2 \sin x \cos x = \sin 2 x

. Answer.
Second - method:-

y = \sin^{2} (x) . we know that. \cos 2 A = 1 - 2 . \sin^{2} (A) . or. \sin^{2} (A) = \frac{1 - \cos 2 A}{2}

y = \frac{1 . - \cos 2 x}{2}

y = \frac{1}{2} . - \frac{1}{2} \cos 2 x

\frac{d y}{d x} = 0 - \frac{1}{2} . (- \sin 2 x) .2

\frac{d y}{d x} = \sin 2 x . Answer.

RizerMix

Expert2021-12-29Added 656 answers

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

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