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## Homework Statement

Hi

Say I have the equality

[tex]

\frac{df(x)}{dx} = \frac{dg(z)}{dz}

[/tex]

where f and g are two functions that are well-behaved such that I can take their derivate. The variables x and z are both real, and run from -∞ to ∞. In this case, am I allowed to divide out the differentials dx and dz such that

[tex]

df(x) = dg(z)

[/tex]

which I can integrate and obtain

[tex]

f(x) = g(z) + \text{constant}

[/tex]

?

Best,

Niles.