Question

Differentiate y=xsinxcosx

Answer 1

Answer:

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Answer 2

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→Differentiate y=xsinxcosx

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⇒$y=Sin\theta .Cos\theta$

⇒$\Large{\frac{dy}{dx}}$

⇒$\frac{d(Sin\theta . Cos\theta)}{dx}$

⇒$Cos\theta \times \frac{d(Sin\theta)}{dx}+ Sin\theta \times \frac{d(Cos\theta)}{dx}$

⇒$Cos\theta \times Cos\theta + Sin\theta \times (-Sin\theta)$

⇒$Cos^2\theta - Sin^2\theta$

⇒$\huge{\pink{\overbrace{\underbrace{Cos^{\small{2}}\theta-Sin^{\small{2}}\theta}}}}$

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Formulas Used :-

$If\:y=u\times v$

⇒$\frac{d(u\times v)}{dx}$

⇒$\fbox{v\frac{du}{dx}+u\frac{dv}{dx}}$

• $\fbox{\frac{d(Sin\theta)}{dx}=Cos\theta}$
• $\fbox{\frac{d(Cos\theta)}{dx}=-Sin\theta}$

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