Question

What is the derivative of `(cos x) / (1-sinx)`?

Answer 1

Use the Quotient Rule:
`y'=(-sinx(1-sinx)+cosx(cosx))/(1-sinx)^2=`
`=(-sinx+sin^2x+cos^2x)/(1-sinx)^2=`
`=(1-sinx)/(1-sinx)^2=1/(1-sinx)`

I used the fact that: `sin^2x+cos^2x=1`