Question

3. Find f'(x) for f(x) = √(5 + e²x)​

Answer 1

Explanation:

We may use the chain rule to find the derivative of f(x) = (5 + e2x). The chain rule asserts that if y = f(u) and u = g(x), then the derivative of y with respect to x is:

dy/dx = dy/du * du/dx

In this situation, let u = 5 + e2x, and we get:

f(u) = √u

And we know that the derivative of u with regard to u is:

df(u)/du = 1/(2*u)

We also know:

du/dx = 2e2x

So, when we plug these into the chain rule, we get:

df(x)/dx = du/dx = 1/(2*u) * 2e2x = e2x/((5 + e2x))

As a result, the derivative of f(x) = (5 + e2x) is:

f'(x) = e2x / (5 + e2x)