The Chain Rule: Finding the Derivative of e^u with Respect to x

derivative of e^u

To find the derivative of the function e^u, where u is a variable, we can use the chain rule

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

(f(g(x)))’ = f'(g(x)) * g'(x)

In this case, f(u) = e^u and g(x) = u. So, we have:

(e^u)’ = (e^u)’ * (u)’

The derivative of e^u with respect to u is simply e^u, since e^u is its own derivative. The derivative of u with respect to x is 1.

Therefore, the derivative of e^u with respect to x is:

(e^u)’ = (e^u) * 1 = e^u

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

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