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Popular >

derivative of arctanh(sqrt(3x))

Solution

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

Solution

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

Solution steps

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

Simplify

arctanh (3 x) : arctanh (3 x)

= \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) = \frac{3}{2 x}

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

Simplify

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

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

Popular Examples

derivative of ln((x^2)/(2x^2+3x+2))derivative of

ln (\frac{x ^{2}}{2 x ^{2} + 3 x + 2})

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\int x - 25 - x^{2} d x

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\int \frac{4 x ^{2} + 2 x - 1}{x ^{3} + x ^{2}} d x

derivative of sqrt(a)-sqrt(x)

\frac{d}{d x} (a - x)

Frequently Asked Questions (FAQ)

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