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Popular Calculus >

derivative of (cot(x)/x)

Solution

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

Solution

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

Solution steps

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

Apply the Quotient Rule:

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

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

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

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

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

Simplify

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

Graph

Popular Examples

derivative of (3+xf(x))/(sqrt(x))

d er i v a t i v e \frac{3 + x f ( x )}{x}

derivative of ln(1-(10/x))

\frac{d}{d x} (ln (1 - \frac{10}{x}))

derivative of f(x)=sqrt(5x+1)

d er i v a t i v e f (x) = 5 x + 1

derivative of f(x)=((tan(x)-1))/(sec(x))

d er i v a t i v e f (x) = \frac{( tan ( x ) - 1 )}{sec ( x )}

integral from 0 to 2 of x^2

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

Frequently Asked Questions (FAQ)

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