en

English

Español

Português

Français

Deutsch

Italiano

Русский

中文(简体)

한국어

日本語

Tiếng Việt

עברית

العربية

Popular >

derivative of ln(1+cos(x))

Solution

\frac{d}{d x} (ln (1 + cos (x)))

Solution

- \frac{sin ( x )}{1 + cos ( x )}

Solution steps

\frac{d}{d x} (ln (1 + cos (x)))

Apply the chain rule:

\frac{1}{1 + cos ( x )} \frac{d}{d x} (1 + cos (x))

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

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

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

Simplify

\frac{1}{1 + cos ( x )} (- sin (x)) : - \frac{sin ( x )}{1 + cos ( x )}

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

Popular Examples

integral from 0 to 1 of xarcsin(x^2)

\int_{0}^{1} x arcsin (x^{2}) d x

derivative of 1200sqrt(x^2-0.1x)

\frac{d}{d x} (1200 x^{2} - 0.1 x)

derivative of 1/(x^3+1)

\frac{d}{d x} (\frac{1}{x ^{3} + 1})

(dy)/(dx)=xy+4x+5y+20

\frac{d y}{d x} = x y + 4 x + 5 y + 20

integral of ((x-2)(x+2))/(x^2)

\int \frac{( x - 2 ) ( x + 2 )}{x ^{2}} d x

Frequently Asked Questions (FAQ)

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