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How many functions exist where their derivative is equal to the original function. For example:

$y = 0$ and $\frac{dy}{dx} = 0$

$y = e^x$ and $\frac{dy}{dx} = e^x$

Are there any other examples of these?

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    Exactly the functions in the form $f_\alpha(x)=\alpha\cdot e^x$ for some $\alpha\in\Bbb R$. How familiar are you with ordinary differential equations? – 2017-01-29
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    you have forgotten to add a constant – 2017-01-29
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    @Dr.SonnhardGraubner No, I did not, because that constant would vanish from the derivative. Or were you talking to the OP? – 2017-01-29

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