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

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

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))(cos(x)+1))

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

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

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{csc ( x ) - cot ( x )}{∣ csc ( x ) - cot ( x ) ∣ ( 1 + cos ( x ) )}

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

Simplify

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

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

y = x^{2} - 2 x, y = 2 - x

\int 3^{4 x + 6} d x

\frac{\partial}{\partial x} (2 y + x^{2} + 1)

2 cos^{2} (t)

y = ln (\frac{x + 3}{x ^{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))(cos(x)+1))
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))(cos(x)+1))