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

d/dx(e^u) u is a function

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

To find the derivative of the function e^u with respect to 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, let’s consider u as a function of x. Therefore, the derivative of e^u with respect to x will be d/dx(e^u). To find it, we need to apply the chain rule.

dy/dx = d/dx(e^u) = e^u * du/dx

Here, e^u is the outer function and du/dx is the inner function. Therefore, we keep e^u the same and multiply it by du/dx.

The second part, du/dx, represents the derivative of u with respect to x. It tells us how the function u changes with respect to x. To find du/dx, you would need to apply the appropriate rules for differentiating the given function u.

So, in summary, the derivative of e^u with respect to x is e^u times the derivative of u with respect to x, du/dx.

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