Question

How to differentiate 2e^y

Answer 1

\[\frac{ d }{ dy }2e^y = 2e^y\]

Answer 2

Remember the derivative of e^x = e^x

Answer 3

Well there's a proof, it requires limits, and \[\frac{ d }{ dx }lnx=\frac{ 1 }{ x }\]

Answer 4

Basically

\[\frac{ d }{ dx } e^x = e^x \implies \frac{ d }{ dx } lnx =\frac{ 1 }{ x }\]

\[\frac{ d }{ dx }(\ln(e^x)) = \frac{ d }{ dx }xlne=\frac{ d }{ dx }x =1 \]

Answer 5

But you can use the chain rule, with the same derivative.

Answer 6

Simpler, I'd say...

Answer 7

\(\Large \color{green}{ლ(́◉◞౪◟◉‵ლ)}\)

Answer 8

\[f(x)=2e^y\\
f'(x)=2e^y\frac{\mathrm d y}{\mathrm dx}\]