What is the derivative of (1-3xarccoth(3x)) ?

The derivative of (1-3xarccoth(3x)) is -3arccoth(3x)+3/(3x+1)

What is the first derivative of (1-3xarccoth(3x)) ?

The first derivative of (1-3xarccoth(3x)) is -3arccoth(3x)+3/(3x+1)

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\frac{d}{d x} ((1 - 3 x) arccoth (3 x))

- 3 arccoth (3 x) + \frac{3}{3 x + 1}

Solution steps

\frac{d}{d x} ((1 - 3 x) arccoth (3 x))

Apply the Product Rule:

(f \cdot g)^{'} = f^{'} \cdot g + f \cdot g^{'}

f = 1 - 3 x, g = arccoth (3 x)

= \frac{d}{d x} (1 - 3 x) arccoth (3 x) + \frac{d}{d x} (arccoth (3 x)) (1 - 3 x)

\frac{d}{d x} (1 - 3 x) = - 3

\frac{d}{d x} (arccoth (3 x)) = \frac{3}{1 - 9 x ^{2}}

= (- 3) arccoth (3 x) + \frac{3}{1 - 9 x ^{2}} (1 - 3 x)

Simplify

(- 3) arccoth (3 x) + \frac{3}{1 - 9 x ^{2}} (1 - 3 x) : - 3 arccoth (3 x) + \frac{3}{3 x + 1}

= - 3 arccoth (3 x) + \frac{3}{3 x + 1}

y^{^{'}} + 4 x y^{3} = 0

\frac{d}{d x} (\frac{4 x ^{3}}{3} + cos (x) + 1)

\frac{d}{d x} (sin (n x))

\frac{\partial}{\partial y} (ln (yz))

\int \frac{1}{x - y} d x

What is the derivative of (1-3xarccoth(3x)) ?
The derivative of (1-3xarccoth(3x)) is -3arccoth(3x)+3/(3x+1)
What is the first derivative of (1-3xarccoth(3x)) ?
The first derivative of (1-3xarccoth(3x)) is -3arccoth(3x)+3/(3x+1)