The Derivative of e^x | Understanding the Chain Rule and Calculation Method for Derivatives

d/dx e^x

To calculate the derivative of e^x with respect to x, denoted as d/dx e^x, we can use the chain rule

To calculate the derivative of e^x with respect to x, denoted as d/dx e^x, we can use the chain rule.

The chain rule states that if we have a composition of functions, the derivative of the composition is the derivative of the outer function multiplied by the derivative of the inner function.

In this case, the outer function is e^x and the inner function is x. The derivative of the inner function with respect to x is 1.

Now, let’s calculate the derivative of the outer function, which is e^x.

The derivative of e^x is the function itself, which is e^x. Therefore, d/dx e^x = e^x.

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

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