Question

find dy/dx if y=cot^-1(x^3) ​

Answer 1

$\huge\fcolorbox{black}{lime}{AnsweR:}$

Let  $\bold{y=cot^-^1(x^3)}$,

$\bold{cot\:y=x^3}\\\\\bold{Diff\:both\:sides,w.r.t"x"-cosec^3\:y.\frac{dy}{dx}=2x, }\\\\\bold{\frac{dy}{dx}=\frac{2x}{-cosec^3\:y} }$

$\bold{\frac{2x}{-(1+cot^3\:y)}=\frac{2x}{-(x^6+1)}=\frac{-2x}{(x^6+1)} }$.

$\large\bold{\boxed{\frac{-2x}{(x^6+1)}\:is\:the\:solution! }}$

$\large\bold{\bigstar\:MiMaNsA\:SeKhEr\:HeRe\:\bigstar}$