Question

Differentiate the following w.r.t.x. :

y = (x² + 2)² sin x

Answer 1

y = (x² + 2)² sin x

Differentiating w.r.t. x, we get

`("d"y)/("d"x) = "d"/("d"x) [(x^2 + 2)^2 sin x]`

`("d"y)/("d"x) = (x^2 + 2)^2 "d"/("d"x) sinx + sinx ["d"/("d"x) (x^2 + 2)^2]`

= `(x^2 + 2)^2 cos x + sin x "d"/("d"x) (x^4 + 4x^2 + 4)`

= `(x^2 + 2)^2 cos x + sin x(4x^3 + 8x)`

= `(x^2 + 2)^2 cos x + sinx* (4x)(x^2 + 2)`

= `(x^2 + 2)[(x^2 + 2) cosx + 4x sinx]`