en

English

Español

Português

Français

Deutsch

Italiano

Русский

中文(简体)

한국어

日本語

Tiếng Việt

עברית

العربية

Popular >

derivative of x/(tan(x))

Solution

\frac{d}{d x} (\frac{x}{tan ( x )})

Solution

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

Solution steps

\frac{d}{d x} (\frac{x}{tan ( x )})

Simplify

\frac{x}{tan ( x )} : x cot (x)

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

Apply the Product Rule:

(f \cdot g)^{'} = f^{'} \cdot g + f \cdot g^{'}

f = x, g = cot (x)

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

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

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

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

Simplify

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

Popular Examples

inverse oflaplace (2e^{-2s})/(s(s+2)(s+3)^2)inverse laplace

\frac{2 e ^{- 2 s}}{s ( s + 2 ) ( s + 3 ) ^{2}}

limit as x approaches a of 2f(x)-3g(x)

x \to a lim (2 f (x) - 3 g (x))

derivative of (sqrt(x^2+a^2)^{e^{x^2}})

\frac{d}{d x} ((x^{2} + a^{2})^{e^{x^{2}}})

d/(dy)((-y)/(x^2+y^2))

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

derivative of log_{2}(3x+1)

\frac{d}{d x} (lo g_{2} (3 x + 1))

Frequently Asked Questions (FAQ)

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