What is the derivative of arctanh(3x) ?

The derivative of arctanh(3x) is 3/(1-9x^2)

What is the first derivative of arctanh(3x) ?

The first derivative of arctanh(3x) is 3/(1-9x^2)

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\frac{d}{d x} (arctanh (3 x))

\frac{3}{1 - 9 x ^{2}}

Solution steps

\frac{d}{d x} (arctanh (3 x))

Apply the chain rule:

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

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

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

= \frac{1}{1 - ( 3 x ) ^{2}} \cdot 3

Simplify

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

= \frac{3}{1 - 9 x ^{2}}

What is the derivative of arctanh(3x) ?
The derivative of arctanh(3x) is 3/(1-9x^2)
What is the first derivative of arctanh(3x) ?
The first derivative of arctanh(3x) is 3/(1-9x^2)