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- Derivative of:
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Derivative of 7/x
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Derivative of z
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Derivative of -2x
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Derivative of 2x^3
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Identical expressions
- x^ two *atanh(x)*acoth(x)
- x squared multiply by hyperbolic tangent of gent of (x) multiply by hyperbolic arcco tangent of gent of (x)
- x to the power of two multiply by hyperbolic tangent of gent of (x) multiply by hyperbolic arcco tangent of gent of (x)
- x2*atanh(x)*acoth(x)
- x2*atanhx*acothx
- x²*atanh(x)*acoth(x)
- x to the power of 2*atanh(x)*acoth(x)
- x^2atanh(x)acoth(x)
- x2atanh(x)acoth(x)
- x2atanhxacothx
- x^2atanhxacothx
Derivative of x^2*atanh(x)*acoth(x)
The solution
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2 x *atanh(x)*acoth(x)
$$x^{2} \operatorname{atanh}{\left(x \right)} \operatorname{acoth}{\left(x \right)}$$
(x^2*atanh(x))*acoth(x)
The first derivative
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/ 2 \ 2 | x | x *atanh(x) |------ + 2*x*atanh(x)|*acoth(x) + ----------- | 2 | 2 \1 - x / 1 - x
$$\frac{x^{2} \operatorname{atanh}{\left(x \right)}}{1 - x^{2}} + \left(\frac{x^{2}}{1 - x^{2}} + 2 x \operatorname{atanh}{\left(x \right)}\right) \operatorname{acoth}{\left(x \right)}$$
The second derivative
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/ / x \ \ | x*|-2*atanh(x) + -------| | |/ 3 \ | 2| 3 | || x 2*x | \ -1 + x / x *atanh(x)| 2*||---------- - ------- + atanh(x)|*acoth(x) + ------------------------- + -----------| || 2 2 | 2 2| ||/ 2\ -1 + x | -1 + x / 2\ | \\\-1 + x / / \-1 + x / /
$$2 \left(\frac{x^{3} \operatorname{atanh}{\left(x \right)}}{\left(x^{2} - 1\right)^{2}} + \frac{x \left(\frac{x}{x^{2} - 1} - 2 \operatorname{atanh}{\left(x \right)}\right)}{x^{2} - 1} + \left(\frac{x^{3}}{\left(x^{2} - 1\right)^{2}} - \frac{2 x}{x^{2} - 1} + \operatorname{atanh}{\left(x \right)}\right) \operatorname{acoth}{\left(x \right)}\right)$$
The third derivative
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/ / / 2 \\ / 2 \ \
| | 2 | 4*x || 2 / x \ 2 | 4*x | |
| | x *|-1 + -------|| 3*x *|-2*atanh(x) + -------| x *|-1 + -------|*atanh(x)|
| | 2 | 2|| 3 | 2| | 2| |
| | 6*x \ -1 + x /| 6*x 3*x \ -1 + x / \ -1 + x / |
-2*|3*atanh(x) + |3 - ------- + -----------------|*acoth(x) - ------- + ---------- + ---------------------------- + --------------------------|
| | 2 2 | 2 2 2 2 |
| \ -1 + x -1 + x / -1 + x / 2\ -1 + x -1 + x |
\ \-1 + x / /
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2
-1 + x
$$- \frac{2 \left(\frac{3 x^{3}}{\left(x^{2} - 1\right)^{2}} + \frac{3 x^{2} \left(\frac{x}{x^{2} - 1} - 2 \operatorname{atanh}{\left(x \right)}\right)}{x^{2} - 1} + \frac{x^{2} \left(\frac{4 x^{2}}{x^{2} - 1} - 1\right) \operatorname{atanh}{\left(x \right)}}{x^{2} - 1} - \frac{6 x}{x^{2} - 1} + \left(\frac{x^{2} \left(\frac{4 x^{2}}{x^{2} - 1} - 1\right)}{x^{2} - 1} - \frac{6 x^{2}}{x^{2} - 1} + 3\right) \operatorname{acoth}{\left(x \right)} + 3 \operatorname{atanh}{\left(x \right)}\right)}{x^{2} - 1}$$
The graph