Differentiate $t a n^{- 1} (a e^{x} . x^{2})$ w.r.t.x

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Solution

$y = t e m^{- 1} [a e^{x} . x^{2}]$

Differentiating w.r.t x

$\frac{d y}{d x} = \frac{1}{1 + (a e^{x} x^{2})^{2}} \times (a e^{2} x^{2} + a e^{x} .2 x)$

= $\frac{a e^{x} (x^{2} + 2 x)}{1 + (a e^{x} x^{2})^{2}}$

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