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

The derivative of arccot(sqrt(2x)) is -1/(sqrt(2)\sqrt{x)(2x+1)}

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

The first derivative of arccot(sqrt(2x)) is -1/(sqrt(2)\sqrt{x)(2x+1)}

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

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

Solution steps

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

Simplify

arccot (2 x) : arccot (2 x)

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

Apply the chain rule:

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

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

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

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

Simplify

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

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

x \to 1 + lim (\frac{x + 10}{x + 3})

\frac{x ^{8} - 2 x ^{4} - 10 x}{x ^{4}}

6 ln (x), x ln (x)

\frac{d}{d t} (- 8 sin (t))

- \frac{5}{x ^{4}}

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