What is the derivative of this function $(cos x) / (1-sinx)$ ?

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Answer 1 · 2017-10-22T11:14:37

$secx(secx+tanx).$

Let, $y=cosx/(1-sinx).$

$:. y=cosx/(1-sinx)xx(1+sinx)/(1+sinx),$

$=(cosx(1+sinx))/(1-sin^2x)=(cosx(1+sinx))/cos^2x.$

$:. y=(1+sinx)/cosx=1/cosx+sinx/cosx, i.e.,$

$y=secx+tanx.$

$rArr dy/dx=secxtanx+sec^2x=secx(tanx+secx).$

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