spaghetti3451
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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?
Partial differentiation when the variable of integration is different
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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,
[tex]\frac{\partial Q^n}{\partial x}= n Q^{n-1}\frac{\partial Q}{\partial x}[/tex]
which is, as tiny-tim said, the same as
[tex]\frac{dQ^n}{dx}= n Q^{n-1}\frac{dQ}{dx}[/tex]
ignoring the other variables.
Assuming that Q is, in fact, a function of x, y, z, etc. then, by the chain rule,
[tex]\frac{\partial Q^n}{\partial x}= n Q^{n-1}\frac{\partial Q}{\partial x}[/tex]
which is, as tiny-tim said, the same as
[tex]\frac{dQ^n}{dx}= n Q^{n-1}\frac{dQ}{dx}[/tex]
ignoring the other variables.