Question

What is the derivative of `(12/sinx) + (1/cotx)`?

Answer 1

`−12cosecx⋅cotx+sec^2x`

Explanation:

1/`sin x` = `cosec x` similarly `1/cotx` = `tanx`
the question changes to `12cosecx+tanx`
the derivative is `-12cosecx*cotx+sec^2x` by (u/v rule of differentiation)
`d/dx` `(1/sinx)` = `1/sin^2x` `(-1*cosx)`
= `-cosx/sinx` `1/sinx`
=`-cosecx cotx`
`d/dx` `tanx`= `d/dx(sinx/cosx)`
=`1/cos^2x` `(cosx*cosx-sinx*(-sinx))`
=`(cos^2x+sin^2x)/cos^2x`
=`1/cos^2x`=`sec^2x`