Question

differention of -r tan nx with respect to x

Answer 1

Are the r and n values constant? If so, we can pull this r outside and not worry about it too much. It won't affect the differentiation process.
\[\Large \left(-r \tan nx\right)' \qquad=\qquad -r\left(\tan nx\right)'\]Do you remember the derivative of tangent?
We'll apply the chain rule after you do that step.

Answer 2

why not..?

Answer 3

I'm pretty sure if this was equation was written in terms of polar coordinates it would have been \(\large r\) and \(\large \theta\), not \(\large r\) and \(\large x\). :)

But whatever, the original poster seems to be away.. -_-