What is the derivative of (cot(x)/(x^2)) ?

The derivative of (cot(x)/(x^2)) is -(xcsc^2(x)+2cot(x))/(x^3)

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

The first derivative of (cot(x)/(x^2)) is -(xcsc^2(x)+2cot(x))/(x^3)

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

- \frac{x csc ^{2} ( x ) + 2 cot ( x )}{x ^{3}}

Solution steps

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

Apply the Quotient Rule:

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

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

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

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

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

Simplify

\frac{( - csc ^{2} ( x ) ) x ^{2} - 2 x cot ( x )}{( x ^{2} ) ^{2}} : - \frac{x csc ^{2} ( x ) + 2 cot ( x )}{x ^{3}}

= - \frac{x csc ^{2} ( x ) + 2 cot ( x )}{x ^{3}}

\frac{d y}{d x} + \frac{1}{x} y = 7 x^{2}

\frac{d}{d x} (\frac{6}{x ^{2} + 1})

\frac{d}{d t} (1 - 3 t)

x e^{- x^{2}}

\int \frac{3 x}{( 2 x ^{2} + 1 ) ^{3}} d x

What is the derivative of (cot(x)/(x^2)) ?
The derivative of (cot(x)/(x^2)) is -(xcsc^2(x)+2cot(x))/(x^3)
What is the first derivative of (cot(x)/(x^2)) ?
The first derivative of (cot(x)/(x^2)) is -(xcsc^2(x)+2cot(x))/(x^3)