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Derivative of x^-6
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Derivative of x^-11
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Derivative of (x+5)/(x+1)
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Identical expressions
- log(two *x- one)*acot(x)
- logarithm of (2 multiply by x minus 1) multiply by arcco tangent of gent of (x)
- logarithm of (two multiply by x minus one) multiply by arcco tangent of gent of (x)
- log(2x-1)acot(x)
- log2x-1acotx
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Similar expressions
- log(2*x+1)*acot(x)
- log(2*x-1)*arccot(x)
- log(2*x-1)*arccotx
Derivative of log(2*x-1)*acot(x)
The solution
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[src]
log(2*x - 1)*acot(x)
$$\log{\left(2 x - 1 \right)} \operatorname{acot}{\left(x \right)}$$
log(2*x - 1)*acot(x)
The first derivative
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log(2*x - 1) 2*acot(x)
- ------------ + ---------
2 2*x - 1
1 + x
$$- \frac{\log{\left(2 x - 1 \right)}}{x^{2} + 1} + \frac{2 \operatorname{acot}{\left(x \right)}}{2 x - 1}$$
The second derivative
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/ 2 2*acot(x) x*log(-1 + 2*x)\ 2*|- ------------------- - ----------- + ---------------| | / 2\ 2 2 | | \1 + x /*(-1 + 2*x) (-1 + 2*x) / 2\ | \ \1 + x / /
$$2 \left(\frac{x \log{\left(2 x - 1 \right)}}{\left(x^{2} + 1\right)^{2}} - \frac{2}{\left(2 x - 1\right) \left(x^{2} + 1\right)} - \frac{2 \operatorname{acot}{\left(x \right)}}{\left(2 x - 1\right)^{2}}\right)$$
The third derivative
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/ / 2 \ \ | | 4*x | | | |-1 + ------|*log(-1 + 2*x) | | | 2| | | 6 8*acot(x) \ 1 + x / 6*x | 2*|-------------------- + ----------- - --------------------------- + --------------------| |/ 2\ 2 3 2 2 | |\1 + x /*(-1 + 2*x) (-1 + 2*x) / 2\ / 2\ | \ \1 + x / \1 + x / *(-1 + 2*x)/
$$2 \left(\frac{6 x}{\left(2 x - 1\right) \left(x^{2} + 1\right)^{2}} - \frac{\left(\frac{4 x^{2}}{x^{2} + 1} - 1\right) \log{\left(2 x - 1 \right)}}{\left(x^{2} + 1\right)^{2}} + \frac{6}{\left(2 x - 1\right)^{2} \left(x^{2} + 1\right)} + \frac{8 \operatorname{acot}{\left(x \right)}}{\left(2 x - 1\right)^{3}}\right)$$