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

The derivative of 2arctanh(sqrt(x)) is 1/(sqrt(x)(1-x))

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

The first derivative of 2arctanh(sqrt(x)) is 1/(sqrt(x)(1-x))

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

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

Solution steps

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

Take the constant out:

(a \cdot f)^{'} = a \cdot f^{'}

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

Apply the chain rule:

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

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

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

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

Simplify

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

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

\frac{y ^{\frac{3}{2}}}{3} - y^{\frac{1}{2}}

f (x) = ln (sinh (x^{2}))

\frac{d}{d x} (e^{2 x} - x)

(\frac{1}{x ^{4}})^{^{'}}

f (x) = arccos (e^{2 x})

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