What is the derivative of $\frac{cos x}{1 - sin x}$ $(cos x) / (1-sinx)$ ?

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Answer 1 · 2015-06-06T20:03:51

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: $sin^2x+cos^2x=1$

What is the derivative of (cos x) / (1-sinx)cosx1−sinx (cos x) / (1-sinx)?