de^x/dx
e^x
The derivative of e^x with respect to x is e^x.
To see why, we can use the definition of the derivative:
(f(x+h) – f(x)) / h as h approaches 0
So for f(x) = e^x,
(f(x+h) – f(x)) / h = (e^(x+h) – e^x) / h
Now we can simplify using some algebra and the properties of exponents:
(e^x * e^h – e^x) / h
Factor out e^x:
e^x * (e^h – 1) / h
Now we can take the limit as h approaches 0:
lim (e^x * (e^h – 1) / h) as h approaches 0
This limit can be evaluated using L’Hopital’s rule, which shows that it equals e^x.
Therefore, the derivative of e^x with respect to x is e^x.
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