Question

differentiate y = cos x ÷ x^3​

Answer 1

Answer:

$\frac{-xsinx-cosx}{x^4}$

Step-by-step explanation:

y = $\frac{cosx}{x^3}$

by applying u/v rule

$\frac{d}{dx} (u/v)=\frac{v\frac{du}{dx}-u\frac{dv}{dx} }{v^2}$

d/dx=(cos x/x³)= x³d/dx(cosx) - cosx d/dx(x³)/(x³)²

                       = x³-sinx-cos x x²/x^6

                       =$\frac{-x^3sinx-cosx x^2}{x^6}$

taking x² common

                     =$\frac{-xsinx-cosx}{x^4}$