Mister Exam
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- Derivative of a implicit defined function
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- Partial derivative of the function
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How to use it?
- Derivative of:
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Derivative of 6^x
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Derivative of (x^2-1)/(x^2+1)
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Derivative of (x+3)/(x-1)
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Derivative of (x-3)^3
- Graphing y =:
- acos(2*x)^(3)
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Identical expressions
- acos(two *x)^(three)
- arc co sinus of e of ine of (2 multiply by x) to the power of (3)
- arc co sinus of e of ine of (two multiply by x) to the power of (three)
- acos(2*x)(3)
- acos2*x3
- acos(2x)^(3)
- acos(2x)(3)
- acos2x3
- acos2x^3
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Similar expressions
- arccos(2*x)^(3)
Derivative of acos(2*x)^(3)
The solution
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3 acos (2*x)
$$\operatorname{acos}^{3}{\left(2 x \right)}$$
d / 3 \ --\acos (2*x)/ dx
$$\frac{d}{d x} \operatorname{acos}^{3}{\left(2 x \right)}$$
The first derivative
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2 -6*acos (2*x) ------------- __________ / 2 \/ 1 - 4*x
$$- \frac{6 \operatorname{acos}^{2}{\left(2 x \right)}}{\sqrt{1 - 4 x^{2}}}$$
The second derivative
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/ 1 x*acos(2*x) \
-24*|--------- + -------------|*acos(2*x)
| 2 3/2|
|-1 + 4*x / 2\ |
\ \1 - 4*x / /
$$- 24 \left(\frac{x \operatorname{acos}{\left(2 x \right)}}{\left(1 - 4 x^{2}\right)^{\frac{3}{2}}} + \frac{1}{4 x^{2} - 1}\right) \operatorname{acos}{\left(2 x \right)}$$
The third derivative
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/ 2 2 2 \ | 2 acos (2*x) 12*x *acos (2*x) 12*x*acos(2*x)| 24*|- ------------- - ------------- - ---------------- + --------------| | 3/2 3/2 5/2 2 | | / 2\ / 2\ / 2\ / 2\ | \ \1 - 4*x / \1 - 4*x / \1 - 4*x / \-1 + 4*x / /
$$24 \left(- \frac{12 x^{2} \operatorname{acos}^{2}{\left(2 x \right)}}{\left(1 - 4 x^{2}\right)^{\frac{5}{2}}} + \frac{12 x \operatorname{acos}{\left(2 x \right)}}{\left(4 x^{2} - 1\right)^{2}} - \frac{\operatorname{acos}^{2}{\left(2 x \right)}}{\left(1 - 4 x^{2}\right)^{\frac{3}{2}}} - \frac{2}{\left(1 - 4 x^{2}\right)^{\frac{3}{2}}}\right)$$
The graph