Mastering the Chain Rule: Finding the Derivative of f(x) = e^x

d/dx[e^x]

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

To find the derivative of the function f(x) = e^x, we can use the chain rule. The chain rule states that if we have a composite function y = f(g(x)), then the derivative of y with respect to x is given by dy/dx = f'(g(x)) * g'(x).

In this case, f(x) = e^x, so we can rewrite the function as y = f(g(x)) = e^x. Here, f(x) = e^x and g(x) = x.

Now, let’s find the derivative of f(x) = e^x:
f'(x) = d/dx(e^x)
To differentiate e^x, we use the fact that the derivative of e^x with respect to x is equal to e^x itself. So, we have:
f'(x) = e^x

Next, let’s find the derivative of g(x) = x:
g'(x) = d/dx(x)
The derivative of x with respect to x is equal to 1. So, we have:
g'(x) = 1

Now, we can apply the chain rule:
dy/dx = f'(g(x)) * g'(x)
dy/dx = e^x * 1
dy/dx = e^x

Therefore, the derivative of f(x) = e^x with respect to x is e^x.

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