Understanding the Chain Rule | Finding the Derivative of e^x Using the Chain Rule

derivative of natural exponents, f(x)= e^x

To find the derivative of the function f(x) = e^x, where e is the base of the natural logarithm, you can use the chain rule

To find the derivative of the function f(x) = e^x, where e is the base of the natural logarithm, you can use the chain rule.

The chain rule states that if you have a composite function, where one function is applied to another function, the derivative is given by the derivative of the outer function times the derivative of the inner function.

In this case, the outer function is the exponential function e^x, and the inner function is x. Recall that the derivative of e^x is e^x itself.

So, applying the chain rule, we get:

f'(x) = (derivative of outer function) * (derivative of inner function)
= (e^x) * (derivative of inner function)

Since the derivative of x with respect to x is simply 1, we have:

f'(x) = e^x

Therefore, the derivative of f(x) = e^x is f'(x) = e^x.

This means that the rate of change of the exponential function e^x at any point x is equal to the value e^x itself.

More Answers:
Understanding Exponential Functions | An Overview of the Math Behind Growth and Decay
Understanding Exponential Growth in the Mathematical Function f(x) = 0.5 * (4)^x
Exponential Functions Explained | Evaluating and Graphing with Examples

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