Find the derivative of (x^2+1 ) x. - Vidyadip

Question

Find the derivative of $\left(x^2+1\right) \cos x$.

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Answer

Let $\quad y=\left(x^2+1\right) \cos x$
$\therefore \quad \frac{d y}{d x}=\frac{d}{d x}\left[\left(x^2+1\right) \cos x\right]$
$\begin{array}{l}=\cos x \frac{d}{d x}\left(x^2+1\right)+\left(x^2+1\right) \frac{d}{d x} \cos x \\ =\cos x \cdot 2 x+\left(x^2+1\right) \cdot(-\sin x) \\ =2 x \cos x-x^2 \sin x-\sin x\end{array}$

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