Find the second order derivative of the given functions.

x cos x

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Solution

Ley y = x cos x

Differentiating twicely w.r.t. x, we get

$\frac{d y}{d x} = \frac{d}{d x} (x c o s x) = x \frac{d}{d x} c o s x + c o s x \frac{d}{d x} (x) = (- x s i n x) + c o s x .1 = - x s i n x + c o s x (U s i n g p r o d u c t r u l e \frac{d}{d x} (u . v) = u \frac{d v}{d x} + v \frac{d u}{d x}) a n d \frac{d^{2} y}{d x^{2}} = \frac{d}{d x} (- x s i n x + c o s x) = - \frac{d}{d x} (x s i n x) + \frac{d}{d x} (c o s x) = - {x c o s x + s i n x .1} - s i n x = - x c o s x - 2 s i n x (U s i n g p r o d u c t r u l e])$

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