# Thread: find the derivative of this function

1. ## find the derivative of this function

how do i do this

find the derivative of this funtion.
y= ln (ln(tanx))

derive the following properties of log x:
a

how do i do this ?

log U/v = log u-log v
a a a

(the a's are the littlle number/letter at the bottom of log)

2. ## Re: find the derivative of this function

Originally Posted by arsenal12345
how do i do this

find the derivative of this funtion.
y= ln (ln(tanx))

derive the following properties of log x:
a

how do i do this ?

log U/v = log u-log v
a a a

(the a's are the littlle number/letter at the bottom of log)
You should use the chain rule. In this case, since you have a composition of another composition, you'll need to use the chain rule twice. So

\displaystyle \displaystyle \begin{align*} \frac{dy}{dx} = \frac{dy}{du} \, \frac{du}{dv} \, \frac{dv}{dx} \end{align*}

where \displaystyle \displaystyle \begin{align*} v = \tan{x} , u = \ln{v} \end{align*} and \displaystyle \displaystyle \begin{align*} y = \ln{u} \end{align*}.

3. ## Re: find the derivative of this function

Originally Posted by Prove It
You should use the chain rule. In this case, since you have a composition of another composition, you'll need to use the chain rule twice. So

\displaystyle \displaystyle \begin{align*} \frac{dy}{dx} = \frac{dy}{du} \, \frac{du}{dv} \, \frac{dv}{dx} \end{align*}

where \displaystyle \displaystyle \begin{align*} v = \tan{x} , u = \ln{v} \end{align*} and \displaystyle \displaystyle \begin{align*} y = \ln{u} \end{align*}.
what about the question below that ?

4. ## Re: find the derivative of this function

Originally Posted by arsenal12345
what about the question below that ?
You're welcome ><

5. ## Re: find the derivative of this function

Originally Posted by Prove It
You're welcome ><
sorry please accept my apologies for my lack of manners