Question

What is the derivative of `f(x)=tan(x)cot(x)`?

Answer 1

`(df(x))/dx=0`

Explanation:

As `f(x)=tanx*cotx=1`, `(df(x))/dx=0`.

However, let us also try using product rule.

`df(x)/dx=cotxd/dx(tanx)+tanxd/dx(cotx)`

= `cotx*sec^2x+tanx*(-csc^2x)`

= `cosx/sinx*1/cos^2x-sinx/cosx*1/sin^2x`

= `1/(sinxcosx)-1/(sinxcosx)=0`