What is the derivative of sqrt((sin(x)/(1-sin(x)))) ?

The derivative of sqrt((sin(x)/(1-sin(x)))) is (cos(x))/(2sqrt(sin(x))(-sin(x)+1)^{3/2)}

What is the first derivative of sqrt((sin(x)/(1-sin(x)))) ?

The first derivative of sqrt((sin(x)/(1-sin(x)))) is (cos(x))/(2sqrt(sin(x))(-sin(x)+1)^{3/2)}

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\frac{d}{d x} (\frac{sin ( x )}{1 - sin ( x )})

\frac{cos ( x )}{2 sin ( x ) ( - sin ( x ) + 1 ) ^{\frac{3}{2}}}

Solution steps

\frac{d}{d x} (\frac{sin ( x )}{1 - sin ( x )})

Apply the chain rule:

\frac{1}{2 \frac{s i n ( x )}{1 - s i n ( x )}} \frac{d}{d x} (\frac{sin ( x )}{1 - sin ( x )})

= \frac{1}{2 \frac{s i n ( x )}{1 - s i n ( x )}} \frac{d}{d x} (\frac{sin ( x )}{1 - sin ( x )})

\frac{d}{d x} (\frac{sin ( x )}{1 - sin ( x )}) = \frac{cos ( x )}{( 1 - sin ( x ) ) ^{2}}

= \frac{1}{2 \frac{s i n ( x )}{1 - s i n ( x )}} \cdot \frac{cos ( x )}{( 1 - sin ( x ) ) ^{2}}

Simplify

\frac{1}{2 \frac{s i n ( x )}{1 - s i n ( x )}} \cdot \frac{cos ( x )}{( 1 - sin ( x ) ) ^{2}} : \frac{cos ( x )}{2 sin ( x ) ( - sin ( x ) + 1 ) ^{\frac{3}{2}}}

= \frac{cos ( x )}{2 sin ( x ) ( - sin ( x ) + 1 ) ^{\frac{3}{2}}}

\frac{\partial}{\partial y} (25 - x^{2} - 5 y)

\int 6 x 1 + x^{2} d x

y^{^{''}} + 20 y^{^{'}} + 500 y = 0

x d y + y d x = 0

\int π t - t^{2} cos (n t) d t

What is the derivative of sqrt((sin(x)/(1-sin(x)))) ?
The derivative of sqrt((sin(x)/(1-sin(x)))) is (cos(x))/(2sqrt(sin(x))(-sin(x)+1)^{3/2)}
What is the first derivative of sqrt((sin(x)/(1-sin(x)))) ?
The first derivative of sqrt((sin(x)/(1-sin(x)))) is (cos(x))/(2sqrt(sin(x))(-sin(x)+1)^{3/2)}