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- Derivative of:
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Derivative of cos3x
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Derivative of xcos^2x
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Derivative of tgx^2
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Derivative of ctg3x*arccos(3x)^2
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Identical expressions
- ctg3x*arccos(3x)^ two
- ctg3x multiply by arc co sinus of e of (3x) squared
- ctg3x multiply by arc co sinus of e of (3x) to the power of two
- ctg3x*arccos(3x)2
- ctg3x*arccos3x2
- ctg3x*arccos(3x)²
- ctg3x*arccos(3x) to the power of 2
- ctg3xarccos(3x)^2
- ctg3xarccos(3x)2
- ctg3xarccos3x2
- ctg3xarccos3x^2
Derivative of ctg3x*arccos(3x)^2
The solution
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2 cot(3*x)*acos (3*x)
$$\cot{\left(3 x \right)} \operatorname{acos}^{2}{\left(3 x \right)}$$
d / 2 \ --\cot(3*x)*acos (3*x)/ dx
$$\frac{d}{d x} \cot{\left(3 x \right)} \operatorname{acos}^{2}{\left(3 x \right)}$$
The first derivative
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2 / 2 \ 6*acos(3*x)*cot(3*x)
acos (3*x)*\-3 - 3*cot (3*x)/ - --------------------
__________
/ 2
\/ 1 - 9*x
$$\left(- 3 \cot^{2}{\left(3 x \right)} - 3\right) \operatorname{acos}^{2}{\left(3 x \right)} - \frac{6 \cot{\left(3 x \right)} \operatorname{acos}{\left(3 x \right)}}{\sqrt{1 - 9 x^{2}}}$$
The second derivative
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/ / 2 \ \ | / 1 3*x*acos(3*x)\ 2 / 2 \ 2*\1 + cot (3*x)/*acos(3*x)| 18*|- |--------- + -------------|*cot(3*x) + acos (3*x)*\1 + cot (3*x)/*cot(3*x) + ---------------------------| | | 2 3/2| __________ | | |-1 + 9*x / 2\ | / 2 | \ \ \1 - 9*x / / \/ 1 - 9*x /
$$18 \left(- \left(\frac{3 x \operatorname{acos}{\left(3 x \right)}}{\left(1 - 9 x^{2}\right)^{\frac{3}{2}}} + \frac{1}{9 x^{2} - 1}\right) \cot{\left(3 x \right)} + \left(\cot^{2}{\left(3 x \right)} + 1\right) \cot{\left(3 x \right)} \operatorname{acos}^{2}{\left(3 x \right)} + \frac{2 \left(\cot^{2}{\left(3 x \right)} + 1\right) \operatorname{acos}{\left(3 x \right)}}{\sqrt{1 - 9 x^{2}}}\right)$$
The third derivative
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/ / 2 \ / 2 \ \ | | acos(3*x) 9*x 27*x *acos(3*x)| / 2 \ / 1 3*x*acos(3*x)\ 2 / 2 \ / 2 \ 6*\1 + cot (3*x)/*acos(3*x)*cot(3*x)| 54*|- |------------- - ------------ + ---------------|*cot(3*x) + 3*\1 + cot (3*x)/*|--------- + -------------| - acos (3*x)*\1 + cot (3*x)/*\1 + 3*cot (3*x)/ - ------------------------------------| | | 3/2 2 5/2 | | 2 3/2| __________ | | |/ 2\ / 2\ / 2\ | |-1 + 9*x / 2\ | / 2 | \ \\1 - 9*x / \-1 + 9*x / \1 - 9*x / / \ \1 - 9*x / / \/ 1 - 9*x /
$$54 \cdot \left(3 \cdot \left(\frac{3 x \operatorname{acos}{\left(3 x \right)}}{\left(1 - 9 x^{2}\right)^{\frac{3}{2}}} + \frac{1}{9 x^{2} - 1}\right) \left(\cot^{2}{\left(3 x \right)} + 1\right) - \left(\cot^{2}{\left(3 x \right)} + 1\right) \left(3 \cot^{2}{\left(3 x \right)} + 1\right) \operatorname{acos}^{2}{\left(3 x \right)} - \left(\frac{27 x^{2} \operatorname{acos}{\left(3 x \right)}}{\left(1 - 9 x^{2}\right)^{\frac{5}{2}}} - \frac{9 x}{\left(9 x^{2} - 1\right)^{2}} + \frac{\operatorname{acos}{\left(3 x \right)}}{\left(1 - 9 x^{2}\right)^{\frac{3}{2}}}\right) \cot{\left(3 x \right)} - \frac{6 \left(\cot^{2}{\left(3 x \right)} + 1\right) \cot{\left(3 x \right)} \operatorname{acos}{\left(3 x \right)}}{\sqrt{1 - 9 x^{2}}}\right)$$
The graph