What is (\partial)/(\partial x)(ln(tan(x))) ?

The answer to (\partial)/(\partial x)(ln(tan(x))) is 2csc(2x)

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(\partial)/(\partial x)(ln(tan(x)))

\frac{\partial}{\partial x} (ln (tan (x)))

2 csc (2 x)

Solution steps

\frac{\partial}{\partial x} (ln (tan (x)))

Apply the chain rule:

\frac{1}{tan ( x )} \frac{\partial}{\partial x} (tan (x))

= \frac{1}{tan ( x )} \frac{\partial}{\partial x} (tan (x))

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

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

Simplify

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

= 2 csc (2 x)

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

\int \frac{1}{x ^{3} + 3 x ^{2} + 7 x + 5} d x

\int_{0}^{1} 2 π (x^{5} - x^{6}) d x

(x y^{3} + x^{2} y)^{3}

x \to 4 lim (f (x))

What is (\partial)/(\partial x)(ln(tan(x))) ?
The answer to (\partial)/(\partial x)(ln(tan(x))) is 2csc(2x)