Partial differentiation when the variable of integration is different

[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?

 

[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

 

[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.