en

English

Español

Português

Français

Deutsch

Italiano

Русский

中文(简体)

한국어

日本語

Tiếng Việt

עברית

العربية

Popular >

derivative of (csc(x)/x)

Solution

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

Solution

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

Solution steps

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

Apply the Quotient Rule:

(\frac{f}{g})^{'} = \frac{f ^{'} \cdot g - g ^{'} \cdot f}{g ^{2}}

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

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

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

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

Simplify

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

Popular Examples

integral of x^3e^3

\int x^{3} e^{3} d x

derivative of f(x)=x^2-sec(x)+1 derivative of

f (x) = x^{2} - sec (x) + 1

laplacetransform tcos(4t)laplace transform

t cos (4 t)

tangent of f(x)=x^3-3x^2-9x+5,\at x=-12 tangent of

f (x) = x^{3} - 3 x^{2} - 9 x + 5, at x = - 12

integral from 0 to 2 of 0

\int_{0}^{2} 0 d x

Frequently Asked Questions (FAQ)

What is the derivative of (csc(x)/x) ?
The derivative of (csc(x)/x) is (-xcot(x)csc(x)-csc(x))/(x^2)
What is the first derivative of (csc(x)/x) ?
The first derivative of (csc(x)/x) is (-xcot(x)csc(x)-csc(x))/(x^2)