Find the second order derivatives of the function given in Exerci… - Vidyadip

Question

Find the second order derivatives of the function given in Exercise:
$\text{x }\cos\text{x}$

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Answer

Let $\text{y}=\text{x}\cos\text{x}$
$\therefore\ \frac{\text{dy}}{\text{dx}}=\text{x}(-\sin\text{x})+\cos\text{x}.1=-\text{x}\sin\text{x}+\cos\text{x}$
and $\frac{\text{d}^2\text{y}}{\text{dx}^2}=-\text{x}\cos\text{x}-\sin\text{x}.1-\sin\text{x}=-\text{x}\cos\text{x}-2\sin\text{x}$

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