What is the derivative of ln(tan(2x)) ?

The derivative of ln(tan(2x)) is 2sec^2(2x)cot(2x)

What is the first derivative of ln(tan(2x)) ?

The first derivative of ln(tan(2x)) is 2sec^2(2x)cot(2x)

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\frac{d}{d x} (ln (tan (2 x)))

2 sec^{2} (2 x) cot (2 x)

Solution steps

\frac{d}{d x} (ln (tan (2 x)))

Apply the chain rule:

\frac{1}{tan ( 2 x )} \frac{d}{d x} (tan (2 x))

= \frac{1}{tan ( 2 x )} \frac{d}{d x} (tan (2 x))

\frac{d}{d x} (tan (2 x)) = sec^{2} (2 x) \cdot 2

= \frac{1}{tan ( 2 x )} sec^{2} (2 x) \cdot 2

Simplify

\frac{1}{tan ( 2 x )} sec^{2} (2 x) \cdot 2 : 2 sec^{2} (2 x) cot (2 x)

= 2 sec^{2} (2 x) cot (2 x)

\frac{\partial}{\partial t} (1 - cos (t))

\frac{d}{d x} (\frac{8}{x ^{7}})

\int \frac{x ^{2} + 4 x + 1}{x + 3} d x

\int_{0}^{1} t^{3} (1 + t^{4})^{3} d t

\frac{d y}{d x} = - 10 x^{4} + 8 x^{3}

What is the derivative of ln(tan(2x)) ?
The derivative of ln(tan(2x)) is 2sec^2(2x)cot(2x)
What is the first derivative of ln(tan(2x)) ?
The first derivative of ln(tan(2x)) is 2sec^2(2x)cot(2x)