Exponetial function (1 Viewer)

[WEMG]

how do i simplify e^lnx so that I can differentiate it?

 

[iSplicer]

how do i simplify e^lnx so that I can differentiate it?

e^ln(x) = x

raising e to some value is the exact opposite of taking the base e logarithm of that same value. So when you do e^ln(y), you're cancelling the operations out effectively, leaving x

so d(e^ln[x])/dx = 1

 

[WEMG]

Yep, I just realised it after doing another question haha

 

[Pwnage101]

Above is correct, but just remember:

For x>0, exp{ln(x)}=x.
For x<=0, exp{ln(x)} is not defined.

[Whereas ln(exp{x})=x for all real x.]

*Here exp{.}=e^.

 

[Gussy Booo]

May I just add that this result is produced due to the fact that the Exponential and Logarithmic function are INVERSE FUNCTIONS.