Derivative of e^x Explained: Power Rule and Simplifications

d/dx e^x

To find the derivative of e^x with respect to x (d/dx e^x), we can use the power rule for differentiation

To find the derivative of e^x with respect to x (d/dx e^x), we can use the power rule for differentiation.

The power rule states that if we have a function of the form f(x) = x^n, then the derivative f'(x) is given by:
f'(x) = n * x^(n-1)

In this case, the function is e^x, which can be written as e^x = x^1. So, applying the power rule, we have:

d/dx e^x = 1 * e^(x-1)

Simplifying further, we have:

d/dx e^x = e^x

Therefore, the derivative of e^x with respect to x is e^x.

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