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) = nxn-1 and $\frac{d}{dx}$(cos.x) = - sin x]
=$-\frac{4a}{x^5}+\frac{2b}{x^3}$ $-$sin x