Question

$\large \bf \purple{ Namaste} \: \pink{Everyone}$


Please give full steps
□ Find
$\bf \frac{ dy }{dx}$

If


$\: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \boxed{ \sf y = x \times {tan}^{- 1} x}$
​

Answer 1

$\tt y = x{tan}^{-1}x \\ \\ \tt \boxed{\bold{\underline{\green{\tt Multiplication\:Rule: \frac{d(uv)}{dx} = \frac{du}{dx}.v + \frac{dv}{dx}.u }}}} \\ \\ \tt \therefore \frac{dy}{dx} = \frac{dx}{dx}.{tan}^{-1}x + \frac{d({tan}^{-1}x)}{dx}.x \\ \\ \therefore \tt \frac{dy}{dx} = {tan}^{-1}x + \frac{x}{1+{x}^{2}} \\ \\ \tt \therefore \boxed{\bold{\underline{\red{\tt \frac{dy}{dx} = {tan}^{-1}x + \frac{x}{1+{x}^{2}} }}}}$