Fundamental theory of calculus

[Froskoy]

Homework Statement

The question:

The function F(θ,k) is defined as

$$F(\theta,k)=\int_0^θ (f(x,k))\mathrm{d}x$$

Find expressions for $\left({\frac{\partial F}{\partial \theta}}\right)_k$ and $\left({\frac{\partial F}{\partial k}}\right)_θ$

Homework Equations

Fundamental theory of calculus
Chain rule?

The Attempt at a Solution

I think $\left({\frac{\partial F}{\partial \theta}}\right)_k$ is just $f(\theta,k)$ - is that correct? or is it $f(\theta,0)$ because $k$ is held constant so when it is differentiated it will be 0.

I'm a little stumped by the second part. Is there some way to re-express it in terms of $\left({\frac{\partial F}{\partial\theta}}\right)_k$ using the chain rule?

 

[Dick]

$f(\theta,k)$ is right for the first part. For the second you'll need to express it as the integral of a partial derivative. See http://en.wikipedia.org/wiki/Leibniz_integral_rule