What is the derivative of y=(1+x^2)/(arccot(x)) ?

The derivative of y=(1+x^2)/(arccot(x)) is (2xarccot(x)+1)/(arccot^2(x))

What is the first derivative of y=(1+x^2)/(arccot(x)) ?

The first derivative of y=(1+x^2)/(arccot(x)) is (2xarccot(x)+1)/(arccot^2(x))

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derivative of

y = \frac{1 + x ^{2}}{arccot ( x )}

\frac{2 x arccot ( x ) + 1}{arccot ^{2} ( x )}

Solution steps

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

Apply the Quotient Rule:

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

= \frac{\frac{d}{d x} ( 1 + x ^{2} ) arccot ( x ) - \frac{d}{d x} ( arccot ( x ) ) ( 1 + x ^{2} )}{( arccot ( x ) ) ^{2}}

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

\frac{d}{d x} (arccot (x)) = - \frac{1}{x ^{2} + 1}

= \frac{2 x arccot ( x ) - ( - \frac{1}{x ^{2} + 1} ) ( 1 + x ^{2} )}{( arccot ( x ) ) ^{2}}

Simplify

\frac{2 x arccot ( x ) - ( - \frac{1}{x ^{2} + 1} ) ( 1 + x ^{2} )}{arccot ^{2} ( x )} : \frac{2 x arccot ( x ) + 1}{arccot ^{2} ( x )}

= \frac{2 x arccot ( x ) + 1}{arccot ^{2} ( x )}

\int_{- 2}^{0} π (2 x^{2} + 4 x + 3)^{2} d x

\frac{d}{d x} (72 x (6 x^{2} + 8)^{5})

\frac{d}{d x} (\frac{5 x - 2}{x ^{2} + 1})

x \to 0 - lim (\frac{x - 59}{x})

\frac{d}{d x} ((4^{\frac{2}{3}} - x^{\frac{2}{3}})^{\frac{3}{2}})

What is the derivative of y=(1+x^2)/(arccot(x)) ?
The derivative of y=(1+x^2)/(arccot(x)) is (2xarccot(x)+1)/(arccot^2(x))
What is the first derivative of y=(1+x^2)/(arccot(x)) ?
The first derivative of y=(1+x^2)/(arccot(x)) is (2xarccot(x)+1)/(arccot^2(x))