I am a little bit confused when it comes to finding the Euler Lagrange equation of the Jacobi equation
$$J(\phi) = \int^b_a f_{uu}\phi^2 + f_{uv}\phi \phi_x + f_{vv}\phi_x^2$$
The Euler Lagrange equation is $$J_\phi - \frac{d}{dx} J_{\phi_x} = 0$$ How do I deal with taking the derivative of $J$ with respect to $\phi$ under the integral?