What is the derivative of arccot(sqrt(x^2+1)) ?

The derivative of arccot(sqrt(x^2+1)) is -x/((x^2+2)sqrt(x^2+1))

What is the first derivative of arccot(sqrt(x^2+1)) ?

The first derivative of arccot(sqrt(x^2+1)) is -x/((x^2+2)sqrt(x^2+1))

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

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

Solution steps

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

Apply the chain rule:

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

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

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

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

Simplify

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

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

\int e^{7 x + 2} d x

\frac{x ^{6} + e ^{x}}{x + 3}

\frac{d}{d x} (\frac{1}{x + y})

\frac{d}{d x} ((3 x^{2} + 2)^{2} (x^{2} - 5 x)^{3})

(1 - x) (x^{2} - 7)^{2}

What is the derivative of arccot(sqrt(x^2+1)) ?
The derivative of arccot(sqrt(x^2+1)) is -x/((x^2+2)sqrt(x^2+1))
What is the first derivative of arccot(sqrt(x^2+1)) ?
The first derivative of arccot(sqrt(x^2+1)) is -x/((x^2+2)sqrt(x^2+1))