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How to use it?
- Derivative of:
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Derivative of 5-7x
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Derivative of sqrt(x-1)/(sqrt(x^2-x)-1)
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Derivative of f(x)=5
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Derivative of 3^(1/x)
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Identical expressions
- one /arccos^2x
- 1 divide by arc co sinus of e of squared x
- one divide by arc co sinus of e of squared x
- 1/arccos2x
- 1/arccos²x
- 1/arccos to the power of 2x
- 1 divide by arccos^2x
Derivative of 1/arccos^2x
The solution
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[src]
1
1*--------
2
acos (x)
$$1 \cdot \frac{1}{\operatorname{acos}^{2}{\left(x \right)}}$$
d / 1 \ --|1*--------| dx| 2 | \ acos (x)/
$$\frac{d}{d x} 1 \cdot \frac{1}{\operatorname{acos}^{2}{\left(x \right)}}$$
The first derivative
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2 ---------------------------- ________ / 2 2 \/ 1 - x *acos(x)*acos (x)
$$\frac{2}{\sqrt{- x^{2} + 1} \operatorname{acos}{\left(x \right)} \operatorname{acos}^{2}{\left(x \right)}}$$
The second derivative
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/ x 3 \
2*|----------- - -----------------|
| 3/2 / 2\ |
|/ 2\ \-1 + x /*acos(x)|
\\1 - x / /
-----------------------------------
3
acos (x)
$$\frac{2 \left(\frac{x}{\left(- x^{2} + 1\right)^{\frac{3}{2}}} - \frac{3}{\left(x^{2} - 1\right) \operatorname{acos}{\left(x \right)}}\right)}{\operatorname{acos}^{3}{\left(x \right)}}$$
The third derivative
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/ 2 \
| 1 3*x 12 9*x |
2*|----------- + ----------- + -------------------- + ------------------|
| 3/2 5/2 3/2 2 |
|/ 2\ / 2\ / 2\ 2 / 2\ |
\\1 - x / \1 - x / \1 - x / *acos (x) \-1 + x / *acos(x)/
-------------------------------------------------------------------------
3
acos (x)
$$\frac{2 \cdot \left(\frac{9 x}{\left(x^{2} - 1\right)^{2} \operatorname{acos}{\left(x \right)}} + \frac{3 x^{2}}{\left(- x^{2} + 1\right)^{\frac{5}{2}}} + \frac{1}{\left(- x^{2} + 1\right)^{\frac{3}{2}}} + \frac{12}{\left(- x^{2} + 1\right)^{\frac{3}{2}} \operatorname{acos}^{2}{\left(x \right)}}\right)}{\operatorname{acos}^{3}{\left(x \right)}}$$
The graph