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

The derivative of (cos(2x)/(sin(2x))) is -csc^2(2x)*2

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

The first derivative of (cos(2x)/(sin(2x))) is -csc^2(2x)*2

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

- csc^{2} (2 x) \cdot 2

Solution steps

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

Simplify

\frac{cos ( 2 x )}{sin ( 2 x )} : cot (2 x)

= \frac{d}{d x} (cot (2 x))

Apply the chain rule:

- csc^{2} (2 x) \frac{d}{d x} (2 x)

= - csc^{2} (2 x) \frac{d}{d x} (2 x)

\frac{d}{d x} (2 x) = 2

= - csc^{2} (2 x) \cdot 2

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