The Chain Rule: Finding the Derivative of f(e×) using Composite Functions

f'(e×)

To find the derivative of f(e×), where f is a function, we can use the chain rule

To find the derivative of f(e×), where f is a function, we can use the chain rule. The chain rule states that if we have a composite function, f(g(x)), then the derivative can be found by multiplying the derivative of the outer function f'(g(x)) with the derivative of the inner function g'(x).

In this case, our function is f(e×). Let’s denote the inner function e× as g(x). Now, g(x) = e× can be rewritten as g(x) = e^x. The derivative of g(x) is g'(x) = d/dx(e^x).

The derivative of e^x is simply e^x itself, so g'(x) = e^x.

Now that we have the derivative of the inner function, we can find the derivative of f(g(x)) using the chain rule. Since the outer function f is not explicitly given, we cannot determine the specific derivative of f(g(x)). However, we can express the derivative using the chain rule as f'(g(x)) * g'(x).

Therefore, f'(e×) = f'(g(x)) * g'(x) = f'(e^x) * e^x.

In summary, the derivative of f(e×) is f'(e^x) * e^x.

More Answers: