Question

Find the second order derivatives of the following function x cos x ?

Answer 1

We have,

\[y = x \cos x\]
\[\text { Differentiating w . r . t . x, we get }\]
\[\frac{d y}{d x} = \cos x - x\sin x\]
\[\text { Differentiating again w . r . t . x, we get }\]
\[\frac{d^2 y}{d x^2} = - \sin x - \sin x - x\cos x\]
\[ = - \left( 2\sin x + x\cos x \right)\]