Question

Find the derivative of the following functions (it is to be understood that $a,b,c,d,p,r$ and $s$ are fixed non-zero constants and $m$ and $n$ are integers) : $\frac{a}{x^4}-\frac{b}{x^2}+\cos x$

Answer 1

Let $f\left(x\right)=\frac{a}{x^4}-\frac{b}{x^2}+\cos x$
$f^{\prime }\left(x\right)=\frac{d}{dx}\left(\frac{a}{x^4}\right)-\frac{d}{dx}\left(\frac{b}{x^2}\right)+\frac{d}{dx}\left(\cos x\right)$
$=a\frac{d}{dx}\left(x^{-4}\right)-b\frac{d}{dx}\left(x^{-2}\right)+\frac{d}{dx}\left(\cos x\right)$
$=a(-4x^{-5})-b(-2x^{-3})+(-\sin x)$
$=\frac{-4a}{x^5}+\frac{2b}{x^3}-\sin x$