What is the derivative of (cos(2x)/(1-sin(2x))) ?

The derivative of (cos(2x)/(1-sin(2x))) is (-2sin(2x)(1-sin(2x))+2cos^2(2x))/((1-sin(2x))^2)

What is the first derivative of (cos(2x)/(1-sin(2x))) ?

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

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

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

Solution steps

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

Apply the Quotient Rule:

(\frac{f}{g})^{'} = \frac{f ^{'} \cdot g - g ^{'} \cdot f}{g ^{2}}

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

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

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

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

Simplify

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

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

x \to 0 lim (\frac{x ^{5} + 7 x}{x})

\int \frac{x ^{2}}{81 + x ^{2}} d x

\int (\frac{x}{4}) d x

3 - 7 x

x \to 0 lim (\frac{∣ 3 x ∣}{x})

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