How do you differentiate $\frac{cos x}{sin x - 2}$ $cosx/(sinx-2)$ ?

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Answer 1 · 2016-11-11T22:04:53

$f (x) = \frac{cos x}{sin x - 2}$ $f(x)=(cosx)/(sinx-2)$

Use quotient rule:
$f'(x)=[(sinx-2)(-sinx)-(cosx)(cosx)]/[(sinx-2)^2]$

$f'(x)=(-sin^2x+2sinx-cos^2x)/(sinx-2)^2$

$f'(x)=(2sinx-(sin^2x+cos^2x))/(sinx-2)^2$

$f'(x)=(2sinx-1)/(sinx-2)^2$

How do you differentiate cosx/(sinx-2)cosxsinx−2cosx/(sinx-2)?