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): (ax2+ sin x)(p+qcos x)

Answer 1

Let f(x)= (ax2 +sinx)(p+1cosx)
By Product rule,
f'(x)= (ax2 +sinx) $\frac{d}{dx}$ (p+1cosx) + (p+1cosx)$\frac{d}{dx}$(ax2 +sinx)
= (ax2 + sinx)(-qsinx) + (p+1cosx)(2ax+cosx)
=-q sinx(ax2+ sinx)+ (p+1cosx)(2ax+cosx)