Derivative of e^x: Exploring the Power Rule in Calculus

Dx {e^x}=?

To find the derivative of the function f(x) = e^x, we can use the power rule

To find the derivative of the function f(x) = e^x, we can use the power rule. Remember that the power rule states that if we have a function of the form f(x) = e^ax, where a is a constant, then its derivative is f'(x) = a * e^ax.

In this case, we have f(x) = e^x. Since there is no coefficient or exponent attached to e, we can consider it as 1 * e^x. Therefore, applying the power rule, we get:

f'(x) = 1 * e^x

Simplifying this, we have:

f'(x) = e^x

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

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