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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