What is the derivative of x+cot(x) ?

The derivative of x+cot(x) is -cot^2(x)

What is the first derivative of x+cot(x) ?

The first derivative of x+cot(x) is -cot^2(x)

English

Español

Português

Français

Deutsch

Italiano

Русский

中文(简体)

한국어

日本語

Tiếng Việt

עברית

العربية

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

- cot^{2} (x)

Solution steps

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

Apply the Sum/Difference Rule:

(f \pm g)^{'} = f^{'} \pm g^{'}

= \frac{d x}{d x} + \frac{d}{d x} (cot (x))

\frac{d x}{d x} = 1

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

= 1 - csc^{2} (x)

Use the Pythagorean identity:

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

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

= - cot^{2} (x)

What is the derivative of x+cot(x) ?
The derivative of x+cot(x) is -cot^2(x)
What is the first derivative of x+cot(x) ?
The first derivative of x+cot(x) is -cot^2(x)