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How to use it?
- Derivative of:
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Derivative of 5*x^2-2/sqrt(x)+sin(pi/4)
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Derivative of 1/3*x^3
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Derivative of x^2/(x^2+1)
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Derivative of x*sqrt(3-x)
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Identical expressions
- ((ctg)^ three (4x))*(arctg(2x))
- ((ctg) cubed (4x)) multiply by (arctg(2x))
- ((ctg) to the power of three (4x)) multiply by (arctg(2x))
- ((ctg)3(4x))*(arctg(2x))
- ctg34x*arctg2x
- ((ctg)³(4x))*(arctg(2x))
- ((ctg) to the power of 3(4x))*(arctg(2x))
- ((ctg)^3(4x))(arctg(2x))
- ((ctg)3(4x))(arctg(2x))
- ctg34xarctg2x
- ctg^34xarctg2x
Derivative of ((ctg)^3(4x))*(arctg(2x))
The solution
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3 cot (x)*4*x*atan(2*x)
$$\cot^{3}{\left(x \right)} 4 x \operatorname{atan}{\left(2 x \right)}$$
d / 3 \ --\cot (x)*4*x*atan(2*x)/ dx
$$\frac{d}{d x} \cot^{3}{\left(x \right)} 4 x \operatorname{atan}{\left(2 x \right)}$$
The first derivative
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3
3 8*x*cot (x) 2 / 2 \
4*cot (x)*atan(2*x) + ----------- + 4*x*cot (x)*\-3 - 3*cot (x)/*atan(2*x)
2
1 + 4*x
$$4 x \left(- 3 \cot^{2}{\left(x \right)} - 3\right) \cot^{2}{\left(x \right)} \operatorname{atan}{\left(2 x \right)} + 4 \cot^{3}{\left(x \right)} \operatorname{atan}{\left(2 x \right)} + \frac{8 x \cot^{3}{\left(x \right)}}{4 x^{2} + 1}$$
The second derivative
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/ 2 2 2 / 2 \ \ |2*cot (x) 8*x *cot (x) / 2 \ 6*x*\1 + cot (x)/*cot(x) / 2 \ / 2 \ | 8*|--------- - ------------ - 3*\1 + cot (x)/*atan(2*x)*cot(x) - ------------------------ + 3*x*\1 + cot (x)/*\1 + 2*cot (x)/*atan(2*x)|*cot(x) | 2 2 2 | | 1 + 4*x / 2\ 1 + 4*x | \ \1 + 4*x / /
$$8 \left(3 x \left(\cot^{2}{\left(x \right)} + 1\right) \left(2 \cot^{2}{\left(x \right)} + 1\right) \operatorname{atan}{\left(2 x \right)} - 3 \left(\cot^{2}{\left(x \right)} + 1\right) \cot{\left(x \right)} \operatorname{atan}{\left(2 x \right)} - \frac{8 x^{2} \cot^{2}{\left(x \right)}}{\left(4 x^{2} + 1\right)^{2}} - \frac{6 x \left(\cot^{2}{\left(x \right)} + 1\right) \cot{\left(x \right)}}{4 x^{2} + 1} + \frac{2 \cot^{2}{\left(x \right)}}{4 x^{2} + 1}\right) \cot{\left(x \right)}$$
The third derivative
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/ / 2 \ \ | 3 | 16*x | | | 8*x*cot (x)*|-1 + --------| | | 3 2 / 2 \ / 2 \ | 2| 2 2 / 2 \ / 2 \ / 2 \ | | 24*x*cot (x) 18*cot (x)*\1 + cot (x)/ / 2 \ |/ 2 \ 4 2 / 2 \| \ 1 + 4*x / / 2 \ / 2 \ 72*x *cot (x)*\1 + cot (x)/ 18*x*\1 + cot (x)/*\1 + 2*cot (x)/*cot(x)| 8*|- ------------ - ------------------------ - 3*x*\1 + cot (x)/*\\1 + cot (x)/ + 2*cot (x) + 7*cot (x)*\1 + cot (x)//*atan(2*x) + --------------------------- + 9*\1 + cot (x)/*\1 + 2*cot (x)/*atan(2*x)*cot(x) + --------------------------- + -----------------------------------------| | 2 2 2 2 2 | | / 2\ 1 + 4*x / 2\ / 2\ 1 + 4*x | \ \1 + 4*x / \1 + 4*x / \1 + 4*x / /
$$8 \cdot \left(- 3 x \left(\cot^{2}{\left(x \right)} + 1\right) \left(2 \cot^{4}{\left(x \right)} + 7 \left(\cot^{2}{\left(x \right)} + 1\right) \cot^{2}{\left(x \right)} + \left(\cot^{2}{\left(x \right)} + 1\right)^{2}\right) \operatorname{atan}{\left(2 x \right)} + 9 \left(\cot^{2}{\left(x \right)} + 1\right) \left(2 \cot^{2}{\left(x \right)} + 1\right) \cot{\left(x \right)} \operatorname{atan}{\left(2 x \right)} + \frac{72 x^{2} \left(\cot^{2}{\left(x \right)} + 1\right) \cot^{2}{\left(x \right)}}{\left(4 x^{2} + 1\right)^{2}} + \frac{18 x \left(\cot^{2}{\left(x \right)} + 1\right) \left(2 \cot^{2}{\left(x \right)} + 1\right) \cot{\left(x \right)}}{4 x^{2} + 1} + \frac{8 x \left(\frac{16 x^{2}}{4 x^{2} + 1} - 1\right) \cot^{3}{\left(x \right)}}{\left(4 x^{2} + 1\right)^{2}} - \frac{24 x \cot^{3}{\left(x \right)}}{\left(4 x^{2} + 1\right)^{2}} - \frac{18 \left(\cot^{2}{\left(x \right)} + 1\right) \cot^{2}{\left(x \right)}}{4 x^{2} + 1}\right)$$
The graph