# Math Help - the reciprocal identity..

1. ## the reciprocal identity..

There is the given. The instruction is to differentiate.

Now my question is, can I do..

..by using the trigonometric reciprocal identity, in which it results to

??? Thanks!

2. Originally Posted by cutiemike1

There is the given. The instruction is to differentiate.

Now my question is, can I do..

..by using the trigonometric reciprocal identity, in which it results to

??? Thanks!
NO. $\displaystyle \frac{1}{\tan^{-1}(4x)} \neq \cot^{-1}(4x)$. Do you realise that $\tan^{-1}(4x)$ means the inverse tan function, NOT the reciprocal tan function.

3. Originally Posted by mr fantastic
NO. $\displaystyle \frac{1}{\tan^{-1}(4x)} \neq \cot^{-1}(4x)$. Do you realise that $\tan^{-1}(4x)$ means the inverse tan function, NOT the reciprocal tan function.
yeah! it boggles my mind, but I know it isn't right..

but on the other hand is it possible to do it in QUOTIENT RULE??

or what could be the correct procedure? may be you can show me the first step only then i will do the rest..include also the answer but not the solution so that i may compare it to what i will do..

4. alright! yeah!.. ) THANKS a LOT skeeter and mr. fantastic.