The Chain Rule: How to Find the Derivative of e^x

(e^x)’

To find the derivative of e^x, we can use the chain rule

To find the derivative of e^x, we can use the chain rule. The chain rule states that if we have a function of the form f(g(x)), where f and g are both differentiable functions, then the derivative of f with respect to x is given by f'(g(x)) times g'(x).

In this case, f(u) = e^u and g(x) = x.

We can start by finding the derivative of f(u) = e^u. The derivative of e^u is simply itself, so f'(u) = e^u.

Next, we find the derivative of g(x) = x. The derivative of x with respect to x is simply 1, so g'(x) = 1.

Now, applying the chain rule, we have:

(e^x)’ = f'(g(x)) * g'(x)
= e^(g(x)) * g'(x)
= e^x * 1
= e^x

Therefore, the derivative of e^x is e^x.

More Answers:

The Law of Exponents: Simplifying the Expression a^(x+y) using the Laws of Exponents
Simplifying Exponential Expression: a^(x-y) Using Exponent Laws
Simplifying (a^x)^y: Exponent Rule for Raising a Power to a Power

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