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)