en

English

Español

Português

Français

Deutsch

Italiano

Русский

中文(简体)

한국어

日本語

Tiếng Việt

עברית

العربية

Popular >

derivative of ln(csc(x+cot(x)))

Solution

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

Solution

- csc (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)) = - cot (x) csc (x) - csc^{2} (x)

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

Simplify

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

= - csc (x)

Graph

Popular Examples

limit as x approaches infinity of-2x+8

x \to \infty lim (- 2 x + 8)

(\partial)/(\partial x)(x/(x^5-y^4))

\frac{\partial}{\partial x} (\frac{x}{x ^{5} - y ^{4}})

integral from-R to R of sqrt(R^2-x^2)

\int_{- R}^{R} R^{2} - x^{2} d x

(\partial)/(\partial y)(xe^{-y/x})

\frac{\partial}{\partial y} (x e^{- \frac{y}{x}})

integral from 1 to infinity of 5/(x^3)

\int_{1}^{\infty} \frac{5}{x ^{3}} d x

Frequently Asked Questions (FAQ)

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