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): \(\frac{a}{x^4}-\frac{b}{x^2}\) + cosx

Answer 1

Let f(x)=- f'(x)= \(\frac{a}{x^4}-\frac{b}{x^2}\) + cosx
f'(x) = \(\frac{d}{dx}\) (\(\frac{a}{x^4}\)-\(\frac{d}{dx}\)(\(\frac{b}{x^2}\)) +\(\frac{d}{dx}\)(cos.x) 
=a \(\frac{d}{dx}\) (x-4) - b\(\frac{d}{dx}\)(x-2) +\(\frac{d}{dx}\)(cos.x)
= a(-4x^-5)-b(-2x ^-3)+(-sin x) [\(\frac{d}{dx}\)(xⁿ) = nx^n-1 and \(\frac{d}{dx}\)(cos.x) = - sin x] 
=\(-\frac{4a}{x^5}+\frac{2b}{x^3}\) \(-\)sin x