Exploring the Chain Rule | Finding the Derivative of e^x with Respect to x

d/dx[e^x]

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

To find the derivative of e^x with respect to x, we can use the chain rule. The chain rule states that if we have a function f(g(x)), the derivative of f with respect to x is given by f'(g(x)) multiplied by g'(x).

In this case, we have f(x) = e^x. The derivative of f(x) with respect to x, denoted as f'(x) or df/dx, is what we need to find. Using the chain rule, we have:

f'(x) = (e^x)’ * (x)

Now, let’s find the derivative of e^x. The derivative of e^x with respect to x can simply be calculated as e^x since the derivative of e^x is itself. Therefore, (e^x)’ = e^x.

Substituting this result back into our equation, we have:

f'(x) = e^x * (x)

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

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