ImmonoKedo8bj

2023-02-26

How to differentiate $y={\mathrm{sin}x}^{2}$?

Elianna Long

Beginner2023-02-27Added 4 answers

$y=\mathrm{sin}\left({x}^{2}\right)$

Applying the chain rule:

$\frac{dy}{dx}=\mathrm{cos}\left({x}^{2}\right)\cdot \frac{d}{dx}\left({x}^{2}\right)$

$=\mathrm{cos}\left({x}^{2}\right)\cdot 2x$ [Power rule]

$=2x\mathrm{cos}\left({x}^{2}\right)$

Answer is $=2x\mathrm{cos}\left({x}^{2}\right)$

Applying the chain rule:

$\frac{dy}{dx}=\mathrm{cos}\left({x}^{2}\right)\cdot \frac{d}{dx}\left({x}^{2}\right)$

$=\mathrm{cos}\left({x}^{2}\right)\cdot 2x$ [Power rule]

$=2x\mathrm{cos}\left({x}^{2}\right)$

Answer is $=2x\mathrm{cos}\left({x}^{2}\right)$