Question

Find the second order derivative of the function.

x . cos x

Answer 1

Let, y = x cos x

Differentiating both sides with respect to x,

`dy/dx = x d/dx cos x + cos x d/dx (x)`

= x (−sin x) + cos x × 1

= −x sin x + cos x

Differentiating both sides again with respect to x,

`(d^2 y)/dx^2 = - [x d/dx sin x + sin x d/dx (x)] + d/dx cos x`

= −[x cos x + sin x × 1] + [−sin x]

= −x cos x − sin x − sin x

= −x cos x + 2 sin x