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): (x²+1) cosx

Answer 1

Let f(x)= (x²+1) cos x
By Product rule,
f'(x)= (x²+1) \(\frac{d}{dx}\) (cos x) + cos x\(\frac{d}{dx}\)(x²+1)
= (x²+1)(-sinx) + cos x(2x)
=-x² sin x -sin x + 2xcos x