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How to use it?
- Derivative of:
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Derivative of -2x/(1+x^2)^2
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Derivative of 3*sin(x)^(2)
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Derivative of log(secx+tanx)
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Derivative of ln(3x-2)
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Identical expressions
- arctanh(4x^(three)+3x- two)
- arc hyperbolic tangent of gent of (4x to the power of (3) plus 3x minus 2)
- arc hyperbolic tangent of gent of (4x to the power of (three) plus 3x minus two)
- arctanh(4x(3)+3x-2)
- arctanh4x3+3x-2
- arctanh4x^3+3x-2
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Similar expressions
- arctanh(4x^(3)-3x-2)
- arctanh(4x^(3)+3x+2)
Derivative of arctanh(4x^(3)+3x-2)
The solution
You have entered
[src]
/ 3 \ atanh\4*x + 3*x - 2/
$$\operatorname{atanh}{\left(4 x^{3} + 3 x - 2 \right)}$$
d / / 3 \\ --\atanh\4*x + 3*x - 2// dx
$$\frac{d}{d x} \operatorname{atanh}{\left(4 x^{3} + 3 x - 2 \right)}$$
The first derivative
[src]
2
3 + 12*x
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2
/ 3 \
1 - \4*x + 3*x - 2/
$$\frac{12 x^{2} + 3}{- \left(4 x^{3} + 3 x - 2\right)^{2} + 1}$$
The second derivative
[src]
/ 2 \
| / 2\ / 3\|
| 3*\1 + 4*x / *\-2 + 3*x + 4*x /|
6*|-4*x + -------------------------------|
| 2 |
| / 3\ |
\ -1 + \-2 + 3*x + 4*x / /
------------------------------------------
2
/ 3\
-1 + \-2 + 3*x + 4*x /
$$\frac{6 \left(\frac{3 \left(4 x^{2} + 1\right)^{2} \cdot \left(4 x^{3} + 3 x - 2\right)}{\left(4 x^{3} + 3 x - 2\right)^{2} - 1} - 4 x\right)}{\left(4 x^{3} + 3 x - 2\right)^{2} - 1}$$
The third derivative
[src]
/ 3 3 2 \
| / 2\ / 2\ / 3\ / 2\ / 3\|
| 9*\1 + 4*x / 36*\1 + 4*x / *\-2 + 3*x + 4*x / 72*x*\1 + 4*x /*\-2 + 3*x + 4*x /|
6*|-4 + ----------------------- - --------------------------------- + ---------------------------------|
| 2 2 2 |
| / 3\ / 2\ / 3\ |
| -1 + \-2 + 3*x + 4*x / | / 3\ | -1 + \-2 + 3*x + 4*x / |
\ \-1 + \-2 + 3*x + 4*x / / /
--------------------------------------------------------------------------------------------------------
2
/ 3\
-1 + \-2 + 3*x + 4*x /
$$\frac{6 \cdot \left(- \frac{36 \left(4 x^{2} + 1\right)^{3} \left(4 x^{3} + 3 x - 2\right)^{2}}{\left(\left(4 x^{3} + 3 x - 2\right)^{2} - 1\right)^{2}} + \frac{72 x \left(4 x^{2} + 1\right) \left(4 x^{3} + 3 x - 2\right)}{\left(4 x^{3} + 3 x - 2\right)^{2} - 1} + \frac{9 \left(4 x^{2} + 1\right)^{3}}{\left(4 x^{3} + 3 x - 2\right)^{2} - 1} - 4\right)}{\left(4 x^{3} + 3 x - 2\right)^{2} - 1}$$
The graph