Question

Differentiate $\frac{x^{2}sinx}{1-x}$ w.r.t $x$

Answer 1

$y=\frac{x^{2}sinx}{1-x}$ using quotient rule of differentiateion.

$\frac{dy}{dx}=\frac{(1-x)\frac{d}{dx}\left(x^{2}sinx\right)-x^{2}sinx\frac{d}{dx}(1-x)}{(1-x{)}^2}$

$=\frac{(1-x)[2xsinx+x^{2}cosx]-x^{2}sinx(-1)}{(1-x{)}^2}$

$=\frac{(2xsinx+x^{2}cosx-2x^{2}sinx-x^{3}cosx+x^{2}sinx)}{(1-x{)}^2}$

$=\frac{-x^{3}cosx+x^2(cosx-sinx)+2xsinx}{(1-x^2)}$