Predict the nature of the curve

Question

$$f(x)=\int_0^{\sqrt{x}}e^{u^2\over x}du$$ Hence predict the graph of $f(x)$:

Answer 1

Hint: The derivative of $f(x)$ can be computed using the Leibniz integral rule.

$$f'(x)=\frac{d}{dx}\int_{0}^{\sqrt{x}}e^{\frac{u^2}{x}}\,du\\ =e^{\frac{(\sqrt{x})^2}{x}}\frac{d}{dx}\left(\sqrt{x}\right)+\int_{0}^{\sqrt{x}}\frac{\partial}{\partial x}\left(e^{\frac{u^2}{x}}\right)\,du.$$