Question

Differenciat: 1/ (1 - 2sinx)

Answer 1

1/(1-2sinx)×1+2sinx/(1+2sinx)
1+2sinx/1

Answer 2

apply u/v rule of differentiation
$\frac{(1 - 2x) \frac{d1}{dx} - 1 \frac{d(1 - 2 \sin(x) )}{dx} }{( {1 - 2 \sin {}^{2} x) }^{2} } \\ \\ = \frac{(1 - 2x)(0) - 1( - 2 \cos(x)}{ {( {1 - 2 \sin {}^{2} x) }^{2} } } \\ = \frac{2 \cos(x) }{ {( {1 - 2 \sin {}^{2} x) }^{2} }}$