TeX source:
\begin{array}{lclcrcl}\quad\mathbb{D} &=& \mathbb{R}_0^+ \\\\f(x) &=& e^{x^2+\sqrt{x}} \\\\\quad g(h(x)) &=& e^{h(x)} & \Rightarrow & g'(h(x)) &=& e^{h(x)} \\\quad h(x) &=& x^2+\sqrt{x} = x^2+x^{\frac{1}{2}} & \Rightarrow & h'(x) &=& 2x+\dfrac{1}{2}x^{-\frac{1}{2}} = 2x+\dfrac{1}{2\sqrt{x}} \\f'(x) &=& e^{x^2+\sqrt{x}}\cdot\left(2x+\dfrac{1}{2\sqrt{x}}\right) \\\\&=&e^{x^2+\sqrt{x}}\cdot\left(2x+\dfrac{\sqrt{x}}{2x}\right)\end{array}