Dx {e^x}=?
To find the derivative of the function f(x) = e^x, we can apply the power rule for differentiation
To find the derivative of the function f(x) = e^x, we can apply the power rule for differentiation.
The power rule states that if we have a function g(x) = a^x, where a is a constant, then the derivative of g(x) is given by:
d/dx (a^x) = a^x * ln(a)
In the case of f(x) = e^x, we have a = e, which is approximately 2.71828. Therefore, the derivative of f(x) = e^x is:
d/dx (e^x) = e^x * ln(e)
Now, the natural logarithm of e (ln(e)) is equal to 1, so we can simplify the expression further:
d/dx (e^x) = e^x * 1
Finally, we can state the derivative of f(x) = e^x as:
d/dx (e^x) = e^x
In conclusion, the derivative of e^x is e^x.
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