Question

Find derivative of $e^{\sqrt{x}}$ with respect to $x^2$

Answer 1

Derivative of $e^{\sqrt{x}}w.r.t.x^2$

$\frac{d\left(e^{\sqrt{x}}\right)}{d\left(x^2\right)}=\frac{d\left(c^{\sqrt{x}}\right)}{dx}\times \frac{1}{\frac{d\left(x^2\right)}{dx}}=A\times B$

$A=\frac{d\left(e^{\sqrt{x}}\right)}{dx}=\frac{e^{\sqrt{x}}}{2\sqrt{x}}$

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

$\frac{d\left(e^{\sqrt{x}}\right)}{d\left(x^2\right)}=\frac{e^{\sqrt{x}}}{2\sqrt{x}}=\sqrt{x}{e}^{\sqrt{x}}$