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- Derivative of:
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Derivative of 4/x^3
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Derivative of x^6/6
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Derivative of x^3/x
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Derivative of (x-3)^4
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Identical expressions
- (arctg(3x)^ nine)/ nine
- (arctg(3x) to the power of 9) divide by 9
- (arctg(3x) to the power of nine) divide by nine
- (arctg(3x)9)/9
- arctg3x9/9
- (arctg(3x)⁹)/9
- arctg3x^9/9
- (arctg(3x)^9) divide by 9
Derivative of (arctg(3x)^9)/9
The solution
You have entered
[src]
9
atan (3*x)
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9
$$\frac{\operatorname{atan}^{9}{\left(3 x \right)}}{9}$$
atan(3*x)^9/9
The first derivative
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8
3*atan (3*x)
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2
1 + 9*x
$$\frac{3 \operatorname{atan}^{8}{\left(3 x \right)}}{9 x^{2} + 1}$$
The second derivative
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7
-18*atan (3*x)*(-4 + 3*x*atan(3*x))
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2
/ 2\
\1 + 9*x /
$$- \frac{18 \left(3 x \operatorname{atan}{\left(3 x \right)} - 4\right) \operatorname{atan}^{7}{\left(3 x \right)}}{\left(9 x^{2} + 1\right)^{2}}$$
The third derivative
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/ 2 2 \
6 | 2 28 72*x*atan(3*x) 36*x *atan (3*x)|
54*atan (3*x)*|- atan (3*x) + -------- - -------------- + ----------------|
| 2 2 2 |
\ 1 + 9*x 1 + 9*x 1 + 9*x /
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2
/ 2\
\1 + 9*x /
$$\frac{54 \left(\frac{36 x^{2} \operatorname{atan}^{2}{\left(3 x \right)}}{9 x^{2} + 1} - \frac{72 x \operatorname{atan}{\left(3 x \right)}}{9 x^{2} + 1} - \operatorname{atan}^{2}{\left(3 x \right)} + \frac{28}{9 x^{2} + 1}\right) \operatorname{atan}^{6}{\left(3 x \right)}}{\left(9 x^{2} + 1\right)^{2}}$$