# Thread: functions using chain rule

1. ## functions using chain rule

i have the function
log (x^2+1)
e

and i believe the answer is

2x
x^2+1

but i am not sure what steps to take to get the answer, can anyone help.

2. Originally Posted by bart 1000
i have the function
log (x^2+1)
e

and i believe the answer is

2x
x^2+1

but i am not sure what steps to take to get the answer, can anyone help.
use the chain rule. it says $\displaystyle \frac d{dx} f(g(x)) = f'(g(x)) \cdot g'(x)$

here your $\displaystyle f(x) = \ln x$ and your $\displaystyle g(x) = x^2 + 1$

what this translates to for the natural log is: $\displaystyle \frac d{dx} \ln u = \frac {u'}u$, where $\displaystyle u$ is a function of $\displaystyle x$

that is, you take the derivative as if the $\displaystyle x^2 + 1$ was a single variable, and then multiply by its derivative, which is $\displaystyle 2x$, when done

3. Hello,
Originally Posted by bart 1000
i have the function
log (x^2+1)
e

and i believe the answer is

2x
x^2+1

but i am not sure what steps to take to get the answer, can anyone help.
In general, let f(x) be a function, $\displaystyle f(x) > 0$
The derivative of $\displaystyle \ln (f(x))$ is, by using chain rule, $\displaystyle \frac{f'(x)}{f(x)}$