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How to use it?
- Derivative of:
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Derivative of 4-2x
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Derivative of 3*cos(3*x)
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Derivative of 3*sin(2*x)
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Derivative of x^2+3*x-1
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Identical expressions
- y=tg^ five (x+ two)*arccos(3x^ two)
- y equally tg to the power of 5(x plus 2) multiply by arc co sinus of e of (3x squared )
- y equally tg to the power of five (x plus two) multiply by arc co sinus of e of (3x to the power of two)
- y=tg5(x+2)*arccos(3x2)
- y=tg5x+2*arccos3x2
- y=tg⁵(x+2)*arccos(3x²)
- y=tg to the power of 5(x+2)*arccos(3x to the power of 2)
- y=tg^5(x+2)arccos(3x^2)
- y=tg5(x+2)arccos(3x2)
- y=tg5x+2arccos3x2
- y=tg^5x+2arccos3x^2
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Similar expressions
- y=tg^5(x-2)*arccos(3x^2)
Derivative of y=tg^5(x+2)*arccos(3x^2)
The solution
You have entered
[src]
5 / 2\ tan (x + 2)*acos\3*x /
$$\tan^{5}{\left(x + 2 \right)} \operatorname{acos}{\left(3 x^{2} \right)}$$
d / 5 / 2\\ --\tan (x + 2)*acos\3*x // dx
$$\frac{d}{d x} \tan^{5}{\left(x + 2 \right)} \operatorname{acos}{\left(3 x^{2} \right)}$$
The first derivative
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5
4 / 2 \ / 2\ 6*x*tan (x + 2)
tan (x + 2)*\5 + 5*tan (x + 2)/*acos\3*x / - ---------------
__________
/ 4
\/ 1 - 9*x
$$- \frac{6 x \tan^{5}{\left(x + 2 \right)}}{\sqrt{1 - 9 x^{4}}} + \left(5 \tan^{2}{\left(x + 2 \right)} + 5\right) \tan^{4}{\left(x + 2 \right)} \operatorname{acos}{\left(3 x^{2} \right)}$$
The second derivative
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/ / 4 \ \
| 2 | 18*x | |
|3*tan (2 + x)*|-1 + ---------| |
| | 4| / 2 \ |
3 | \ -1 + 9*x / / 2 \ / 2 \ / 2\ 30*x*\1 + tan (2 + x)/*tan(2 + x)|
2*tan (2 + x)*|------------------------------ + 5*\1 + tan (2 + x)/*\2 + 3*tan (2 + x)/*acos\3*x / - ---------------------------------|
| __________ __________ |
| / 4 / 4 |
\ \/ 1 - 9*x \/ 1 - 9*x /
$$2 \left(- \frac{30 x \left(\tan^{2}{\left(x + 2 \right)} + 1\right) \tan{\left(x + 2 \right)}}{\sqrt{1 - 9 x^{4}}} + 5 \left(\tan^{2}{\left(x + 2 \right)} + 1\right) \left(3 \tan^{2}{\left(x + 2 \right)} + 2\right) \operatorname{acos}{\left(3 x^{2} \right)} + \frac{3 \cdot \left(\frac{18 x^{4}}{9 x^{4} - 1} - 1\right) \tan^{2}{\left(x + 2 \right)}}{\sqrt{1 - 9 x^{4}}}\right) \tan^{3}{\left(x + 2 \right)}$$
The third derivative
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/ / 4 \ / 4 \ \
| 2 / 2 \ | 18*x | 3 3 | 54*x | |
| 45*tan (2 + x)*\1 + tan (2 + x)/*|-1 + ---------| 54*x *tan (2 + x)*|-5 + ---------| |
| / 2 \ | 4| | 4| / 2 \ / 2 \ |
2 | / 2 \ | 4 / 2 \ 2 / 2 \| / 2\ \ -1 + 9*x / \ -1 + 9*x / 90*x*\1 + tan (2 + x)/*\2 + 3*tan (2 + x)/*tan(2 + x)|
2*tan (2 + x)*|5*\1 + tan (2 + x)/*\2*tan (2 + x) + 6*\1 + tan (2 + x)/ + 13*tan (2 + x)*\1 + tan (2 + x)//*acos\3*x / + ------------------------------------------------- + ---------------------------------- - -----------------------------------------------------|
| __________ 3/2 __________ |
| / 4 / 4\ / 4 |
\ \/ 1 - 9*x \1 - 9*x / \/ 1 - 9*x /
$$2 \cdot \left(\frac{54 x^{3} \cdot \left(\frac{54 x^{4}}{9 x^{4} - 1} - 5\right) \tan^{3}{\left(x + 2 \right)}}{\left(1 - 9 x^{4}\right)^{\frac{3}{2}}} - \frac{90 x \left(\tan^{2}{\left(x + 2 \right)} + 1\right) \left(3 \tan^{2}{\left(x + 2 \right)} + 2\right) \tan{\left(x + 2 \right)}}{\sqrt{1 - 9 x^{4}}} + 5 \left(\tan^{2}{\left(x + 2 \right)} + 1\right) \left(6 \left(\tan^{2}{\left(x + 2 \right)} + 1\right)^{2} + 13 \left(\tan^{2}{\left(x + 2 \right)} + 1\right) \tan^{2}{\left(x + 2 \right)} + 2 \tan^{4}{\left(x + 2 \right)}\right) \operatorname{acos}{\left(3 x^{2} \right)} + \frac{45 \cdot \left(\frac{18 x^{4}}{9 x^{4} - 1} - 1\right) \left(\tan^{2}{\left(x + 2 \right)} + 1\right) \tan^{2}{\left(x + 2 \right)}}{\sqrt{1 - 9 x^{4}}}\right) \tan^{2}{\left(x + 2 \right)}$$
The graph