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Popular >

derivative of (1+cos(2x)/(1-cos(2x)))

Solution

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

Solution

- 2 csc^{2} (x) cot (x)

Solution steps

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

Simplify

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

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

Apply the chain rule:

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

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

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

= 2 cot (x) (- csc^{2} (x))

Simplify

= - 2 csc^{2} (x) cot (x)

Popular Examples

integral of xsin(1/7 x)

\int x sin (\frac{1}{7} x) d x

integral of 40x^{3/2}-60x^2

\int 40 x^{\frac{3}{2}} - 60 x^{2} d x

derivative of 4/(t^2)derivative of

\frac{4}{t ^{2}}

inverse oflaplace s/(s^2+s+3)inverse laplace

\frac{s}{s ^{2} + s + 3}

derivative of 4/3 pi{r}(x(x)^3)

\frac{d}{d x} (\frac{4}{3} π r (x) (x)^{3})

Frequently Asked Questions (FAQ)

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