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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1Exactly 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? – Jan 29 '17 at 11:29
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you have forgotten to add a constant – Dr. Sonnhard Graubner Jan 29 '17 at 11:29
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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? – Jan 29 '17 at 11:31