3. (10 points) Evaluate $\left.\dfrac{\partial u}{\partial x}\right|_{(0,1)}$ for

$$u(x,y)=\left(e^x-\frac{y}{6}\right)\int_{-2}^{2x} \sqrt{4-t^2}\, dt.$$

Note: Answer must in numerical expression and natural constants like $\pi$, $e$, … etc.