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

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

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

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

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Popular >

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

\frac{- cot ( x ) csc ( x ) - sec ^{2} ( x )}{csc ( x ) - tan ( x )}

Solution steps

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

Apply the chain rule:

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

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

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

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

Simplify

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

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

x \to - \infty lim (\frac{1}{x} + 3)

\frac{d}{d x} (4 x e^{3 x})

\frac{d}{d x} (\frac{x}{sin ( x ) + cos ( x )})

\frac{d}{d x} (e^{5 x} cos (3 x))

\frac{d}{d x} (\frac{x ^{4}}{3 - x ^{3}})

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