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How to use it?
- Derivative of:
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Derivative of 2^(3*x)
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Derivative of -2/x
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Derivative of sin(x)*cos(x)
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Derivative of 1/cos(x)
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Identical expressions
- е^ctg two x/arctg3x^2
- е to the power of ctg2x divide by arctg3x squared
- е to the power of ctg two x divide by arctg3x squared
- еctg2x/arctg3x2
- е^ctg2x/arctg3x²
- е to the power of ctg2x/arctg3x to the power of 2
- е^ctg2x divide by arctg3x^2
Derivative of е^ctg2x/arctg3x^2
The solution
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[src]
cot(2*x)
e
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2
atan (3*x)
$$\frac{e^{\cot{\left(2 x \right)}}}{\operatorname{atan}^{2}{\left(3 x \right)}}$$
/ cot(2*x) \ d |e | --|----------| dx| 2 | \atan (3*x)/
$$\frac{d}{d x} \frac{e^{\cot{\left(2 x \right)}}}{\operatorname{atan}^{2}{\left(3 x \right)}}$$
The first derivative
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/ 2 \ cot(2*x) cot(2*x)
\-2 - 2*cot (2*x)/*e 6*e
---------------------------- - ---------------------
2 / 2\ 3
atan (3*x) \1 + 9*x /*atan (3*x)
$$\frac{\left(- 2 \cot^{2}{\left(2 x \right)} - 2\right) e^{\cot{\left(2 x \right)}}}{\operatorname{atan}^{2}{\left(3 x \right)}} - \frac{6 e^{\cot{\left(2 x \right)}}}{\left(9 x^{2} + 1\right) \operatorname{atan}^{3}{\left(3 x \right)}}$$
The second derivative
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/ / 1 \\
| / 2 \ 27*|--------- + 2*x||
| / 2 \ / 2 \ 12*\1 + cot (2*x)/ \atan(3*x) /| cot(2*x)
2*|2*\1 + cot (2*x)/*\1 + cot (2*x) + 2*cot(2*x)/ + -------------------- + ---------------------|*e
| / 2\ 2 |
| \1 + 9*x /*atan(3*x) / 2\ |
\ \1 + 9*x / *atan(3*x)/
-----------------------------------------------------------------------------------------------------------
2
atan (3*x)
$$\frac{2 \cdot \left(\frac{27 \cdot \left(2 x + \frac{1}{\operatorname{atan}{\left(3 x \right)}}\right)}{\left(9 x^{2} + 1\right)^{2} \operatorname{atan}{\left(3 x \right)}} + 2 \left(\cot^{2}{\left(2 x \right)} + 1\right) \left(\cot^{2}{\left(2 x \right)} + 2 \cot{\left(2 x \right)} + 1\right) + \frac{12 \left(\cot^{2}{\left(2 x \right)} + 1\right)}{\left(9 x^{2} + 1\right) \operatorname{atan}{\left(3 x \right)}}\right) e^{\cot{\left(2 x \right)}}}{\operatorname{atan}^{2}{\left(3 x \right)}}$$
The third derivative
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/ / 2 \ \
| | 6 36*x 27*x | |
| 27*|-1 + --------------------- + -------- + --------------------| / 2 \ / 1 \|
| / 2 \ | / 2\ 2 2 / 2\ | / 2 \ / 2 \ 81*\1 + cot (2*x)/*|--------- + 2*x||
| / 2 \ | / 2 \ 2 / 2 \ | \ \1 + 9*x /*atan (3*x) 1 + 9*x \1 + 9*x /*atan(3*x)/ 18*\1 + cot (2*x)/*\1 + cot (2*x) + 2*cot(2*x)/ \atan(3*x) /| cot(2*x)
-4*|2*\1 + cot (2*x)/*\2 + \1 + cot (2*x)/ + 6*cot (2*x) + 6*\1 + cot (2*x)/*cot(2*x)/ + ----------------------------------------------------------------- + ----------------------------------------------- + ------------------------------------|*e
| 2 / 2\ 2 |
| / 2\ \1 + 9*x /*atan(3*x) / 2\ |
\ \1 + 9*x / *atan(3*x) \1 + 9*x / *atan(3*x) /
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2
atan (3*x)
$$- \frac{4 \cdot \left(\frac{81 \cdot \left(2 x + \frac{1}{\operatorname{atan}{\left(3 x \right)}}\right) \left(\cot^{2}{\left(2 x \right)} + 1\right)}{\left(9 x^{2} + 1\right)^{2} \operatorname{atan}{\left(3 x \right)}} + 2 \left(\cot^{2}{\left(2 x \right)} + 1\right) \left(\left(\cot^{2}{\left(2 x \right)} + 1\right)^{2} + 6 \left(\cot^{2}{\left(2 x \right)} + 1\right) \cot{\left(2 x \right)} + 6 \cot^{2}{\left(2 x \right)} + 2\right) + \frac{18 \left(\cot^{2}{\left(2 x \right)} + 1\right) \left(\cot^{2}{\left(2 x \right)} + 2 \cot{\left(2 x \right)} + 1\right)}{\left(9 x^{2} + 1\right) \operatorname{atan}{\left(3 x \right)}} + \frac{27 \cdot \left(\frac{36 x^{2}}{9 x^{2} + 1} + \frac{27 x}{\left(9 x^{2} + 1\right) \operatorname{atan}{\left(3 x \right)}} - 1 + \frac{6}{\left(9 x^{2} + 1\right) \operatorname{atan}^{2}{\left(3 x \right)}}\right)}{\left(9 x^{2} + 1\right)^{2} \operatorname{atan}{\left(3 x \right)}}\right) e^{\cot{\left(2 x \right)}}}{\operatorname{atan}^{2}{\left(3 x \right)}}$$
The graph