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

d/dx(e^u)

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

To find the derivative of the function f(u) = e^u with respect to x, we can use the chain rule. The chain rule states that if we have a function of the form f(g(x)), then the derivative of f with respect to x is equal to the derivative of f with respect to g, multiplied by the derivative of g with respect to x.

In this scenario, let u = g(x), so we can rewrite the function f(u) = e^u as f(g(x)) = e^g(x).

Applying the chain rule, we have:

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

The first term on the right side of the equation is the derivative of e^u with respect to u. Since the derivative of e^u is simply e^u, we have:

d/du(e^u) = e^u.

The second term on the right side of the equation is the derivative of u with respect to x. This is simply du/dx = 1, since u does not depend on x.

Putting it all together, we have:

d/dx(e^u) = e^u * 1.

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

More Answers: