Derivative of e^g(x) using the chain rule | Step-by-step guide and general form

Derivative of e^g(x)

To find the derivative of the function, e^g(x), we can apply the chain rule of differentiation

To find the derivative of the function, e^g(x), we can apply the chain rule of differentiation.

The chain rule states that if we have a composite function, g(f(x)), the derivative is given by the derivative of the outer function evaluated at the inner function, multiplied by the derivative of the inner function.

In this case, the outer function is e^x, and the inner function is g(x). So, we have:

d/dx (e^g(x)) = d/dg (e^g(x)) * d/dx (g(x))

Let’s first find the derivative of the outer function, e^x. The derivative of e^x with respect to x is simply e^x, as the derivative of e^x is equal to the function itself.

Now, let’s find the derivative of the inner function, g(x), with respect to x. This will vary depending on the specific form of g(x) and will require using additional rules of differentiation.

Once you determine the derivative of g(x), multiply it by e^g(x) to obtain the derivative of e^g(x).

In summary, the derivative of e^g(x) is given by:

d/dx (e^g(x)) = e^g(x) * d/dx (g(x))

Note that this is a general form and the specific derivative will vary depending on the expression for g(x). So, you need to determine the function g(x) to find the derivative of e^g(x) accurately.

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