# Partial differentiation when the variable of integration is different

1. Aug 3, 2011

### spaghetti3451

Consider the partial differential of Q to the power of n w.r.t. x. How would you rearrange this expression so that it contains a partial derivative of Q w.r.t. x?

2. Aug 3, 2011

### tiny-tim

hi failexam!

(have a curly d: ∂ )

do you mean ∂Qn/∂x and ∂Q/∂x ?

it's the same as with dQn/dx and dQ/dx

3. Aug 3, 2011

### HallsofIvy

You talk about "partial derivative" but have only the single variable x.

Assuming that Q is, in fact, a function of x, y, z, etc. then, by the chain rule,
$$\frac{\partial Q^n}{\partial x}= n Q^{n-1}\frac{\partial Q}{\partial x}$$
which is, as tiny-tim said, the same as
$$\frac{dQ^n}{dx}= n Q^{n-1}\frac{dQ}{dx}$$
ignoring the other variables.