1. ## Function derivative

I am going through a practice exam and the following question has me perplexed:

Determine the derivative, with respect to the variable x, of each function below:

A) f(x) = e^x/(1+e^x)

B) f(x) = ln(1+x^2)

I understand the principles of functions, however the "e" is throwing me off in relation. What formulas should I use to solve and what steps to get the correct answers?

Thank you,

Matty

2. Originally Posted by AnAmericanInNederlands25
I am going through a practice exam and the following question has me perplexed:

Determine the derivative, with respect to the variable x, of each function below:

A) f(x) = e^x/(1+e^x)
Use the quotient rule and the fact that the derivative of $e^x$ is just $e^x$

B) f(x) = ln(1+x^2)
Use the chain rule and the fact that the derivative of ln(x) is just $\frac{1}{x}$

I understand the principles of functions, however the "e" is throwing me off in relation. What formulas should I use to solve and what steps to get the correct answers?

Thank you,

Matty

3. I guess I am still confused by what that means exactly... Sorry...

4. Originally Posted by AnAmericanInNederlands25
I guess I am still confused by what that means exactly... Sorry...
$f(x) = \frac{e^x}{1 + e^x}$

note that the derivative of $e^x$ is $e^x$ , then use the quotient rule ...

$f'(x) = \frac{(1+e^x)e^x - e^x(e^x)}{(1+e^x)^2}$

now clean up the algebra

$f(x) = \ln(1+x^2)$

note that $\frac{d}{dx} \ln(u) = \frac{1}{u} \cdot \frac{du}{dx}$

$f'(x) = \frac{2x}{1+x^2}$