What is the derivative of ln(csc(x)-cot(x)) ?

The derivative of ln(csc(x)-cot(x)) is 1/((csc(x)-cot(x))(1+cos(x)))

What is the first derivative of ln(csc(x)-cot(x)) ?

The first derivative of ln(csc(x)-cot(x)) is 1/((csc(x)-cot(x))(1+cos(x)))

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derivative of

ln (csc (x) - cot (x))

\frac{1}{( csc ( x ) - cot ( x ) ) ( 1 + cos ( x ) )}

Solution steps

\frac{d}{d x} (ln (csc (x) - cot (x)))

Apply the chain rule:

\frac{1}{csc ( x ) - cot ( x )} \frac{d}{d x} (csc (x) - cot (x))

= \frac{1}{csc ( x ) - cot ( x )} \frac{d}{d x} (csc (x) - cot (x))

\frac{d}{d x} (csc (x) - cot (x)) = \frac{1}{1 + cos ( x )}

= \frac{1}{csc ( x ) - cot ( x )} \cdot \frac{1}{1 + cos ( x )}

Simplify

\frac{1}{csc ( x ) - cot ( x )} \cdot \frac{1}{1 + cos ( x )} : \frac{1}{( csc ( x ) - cot ( x ) ) ( 1 + cos ( x ) )}

= \frac{1}{( csc ( x ) - cot ( x ) ) ( 1 + cos ( x ) )}

\int \frac{x + 5}{x ^{2} - 16} d x

x \to 0 lim (x^{x^{6}})

f (x) = \frac{x ^{6}}{8 ^{x}}

\frac{\partial}{\partial x} (4 x^{2} cos (x y))

\frac{d}{d x} (\frac{20 x}{( x ^{2} - 4 ) ^{2}})

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