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

d/dx e^u

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

To find the derivative of e^u with respect to x, we can use the chain rule. The chain rule states that if y = f(u) and u = g(x), then the derivative of y with respect to x is given by dy/dx = dy/du * du/dx. In this case, e^u can be considered as y and u as g(x).

So, let’s apply the chain rule to find the derivative of e^u:

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

To differentiate e^u with respect to u, we simply take the derivative of e^u, which is itself:

dy/du = e^u

Now, we need to find du/dx. Since u is a function of x, we can differentiate u with respect to x:

du/dx = d/dx (g(x))

Depending on the specific function g(x), the derivative can be found accordingly. For example, if u = x^2, then du/dx would be 2x.

Finally, we can combine the derivatives using the chain rule formula:

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

Therefore, the derivative of e^u with respect to x is (e^u) * (du/dx).

More Answers: