d/dx eˣ
eˣ
The derivative of eˣ with respect to x is eˣ.
To see why, we can use the definition of the derivative:
f'(x) = lim(h -> 0) [f(x+h) – f(x)] / h
In this case, let f(x) = eˣ. Then we have:
f'(x) = lim(h -> 0) [e^(x+h) – e^x] / h
We can simplify this by factoring out e^x from the numerator:
f'(x) = lim(h -> 0) e^x [e^h – 1] / h
Now we can use the limit definition of e^h as h approaches 0:
lim(h -> 0) [e^h – 1] / h = 1
Therefore, we have:
f'(x) = e^x
So the derivative of eˣ with respect to x is eˣ.
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