Question

Find the derivative of the following functions (it is to be understood that a, b, c, d, p, q, r and s are fixed nonzero constants and m and n are integers): x4(5sinx - 3cosx)

Answer 1

Let f(x)= x4 (5 sin x - 3 cos x)
By Product rule,
f'(x)= x4 $\frac{d}{dx}$ (5sin x-3cosx) + (5sinx-3cosx)$\frac{d}{dx}$(x4)
= x4[5$\frac{d}{dx}$(sin x) - 3$\frac{d}{dx}$ (cos x)] + (5sinx-3cos x)$\frac{d}{dx}$(x4)
=x4[5cosx-3(-sinx)]+ (5 sin x - 3 cos x)(4x3)
=x3[5xcosx + 3xsinx +20sinx -12cosx]