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

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

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

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

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

- \frac{x}{∣ x ∣ ( x ^{2} + 1 )}

Solution steps

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

Apply the chain rule:

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

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

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

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

Simplify

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

= - \frac{x}{∣ x ∣ ( x ^{2} + 1 )}

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

f (x) = x^{3} - 12 x^{2} + 45 x

\int \frac{x ^{2}}{2 x - 1} d x

\int x (4 - x) d x

f (x) = (\frac{x}{1 + x})^{5}, at x = 1

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