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How to use it?
- Derivative of:
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Derivative of 2/x^2
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Derivative of 2*sqrt(x)
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Derivative of x^10
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Derivative of (x+2)^2
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Identical expressions
- (arccosx^ two)/(one -x^ four)
- (arc co sinus of e of x squared ) divide by (1 minus x to the power of 4)
- (arc co sinus of e of x to the power of two) divide by (one minus x to the power of four)
- (arccosx2)/(1-x4)
- arccosx2/1-x4
- (arccosx²)/(1-x⁴)
- (arccosx to the power of 2)/(1-x to the power of 4)
- arccosx^2/1-x^4
- (arccosx^2) divide by (1-x^4)
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Similar expressions
- (arccosx^2)/(1+x^4)
Derivative of (arccosx^2)/(1-x^4)
The solution
You have entered
[src]
2
acos (x)
--------
4
1 - x
$$\frac{\operatorname{acos}^{2}{\left(x \right)}}{1 - x^{4}}$$
/ 2 \ d |acos (x)| --|--------| dx| 4 | \ 1 - x /
$$\frac{d}{d x} \frac{\operatorname{acos}^{2}{\left(x \right)}}{1 - x^{4}}$$
The first derivative
[src]
3 2
2*acos(x) 4*x *acos (x)
- -------------------- + -------------
________ 2
/ 2 / 4\ / 4\
\/ 1 - x *\1 - x / \1 - x /
$$\frac{4 x^{3} \operatorname{acos}^{2}{\left(x \right)}}{\left(1 - x^{4}\right)^{2}} - \frac{2 \operatorname{acos}{\left(x \right)}}{\sqrt{1 - x^{2}} \cdot \left(1 - x^{4}\right)}$$
The second derivative
[src]
/ / 4 \\
| 2 2 | 8*x ||
| 2*x *acos (x)*|-3 + -------||
| 3 | 4||
| 1 x*acos(x) 8*x *acos(x) \ -1 + x /|
2*|------- + ----------- - --------------------- - ----------------------------|
| 2 3/2 ________ 4 |
|-1 + x / 2\ / 2 / 4\ -1 + x |
\ \1 - x / \/ 1 - x *\-1 + x / /
--------------------------------------------------------------------------------
4
-1 + x
$$\frac{2 \left(- \frac{8 x^{3} \operatorname{acos}{\left(x \right)}}{\sqrt{1 - x^{2}} \left(x^{4} - 1\right)} - \frac{2 x^{2} \cdot \left(\frac{8 x^{4}}{x^{4} - 1} - 3\right) \operatorname{acos}^{2}{\left(x \right)}}{x^{4} - 1} + \frac{x \operatorname{acos}{\left(x \right)}}{\left(1 - x^{2}\right)^{\frac{3}{2}}} + \frac{1}{x^{2} - 1}\right)}{x^{4} - 1}$$
The third derivative
[src]
/ / 4 8 \ \
| 3 / 1 x*acos(x) \ 2 | 12*x 16*x | / 4 \ |
| 12*x *|------- + -----------| 12*x*acos (x)*|1 - ------- + ----------| 2 | 8*x | |
| | 2 3/2| | 4 2| 12*x *|-3 + -------|*acos(x)|
| |-1 + x / 2\ | 2 | -1 + x / 4\ | | 4| |
| acos(x) 3*x \ \1 - x / / 3*x *acos(x) \ \-1 + x / / \ -1 + x / |
2*|----------- - ---------- - ----------------------------- + ------------ + ---------------------------------------- + ----------------------------|
| 3/2 2 4 5/2 4 ________ |
|/ 2\ / 2\ -1 + x / 2\ -1 + x / 2 / 4\ |
\\1 - x / \-1 + x / \1 - x / \/ 1 - x *\-1 + x / /
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4
-1 + x
$$\frac{2 \left(- \frac{12 x^{3} \left(\frac{x \operatorname{acos}{\left(x \right)}}{\left(1 - x^{2}\right)^{\frac{3}{2}}} + \frac{1}{x^{2} - 1}\right)}{x^{4} - 1} + \frac{12 x^{2} \cdot \left(\frac{8 x^{4}}{x^{4} - 1} - 3\right) \operatorname{acos}{\left(x \right)}}{\sqrt{1 - x^{2}} \left(x^{4} - 1\right)} + \frac{3 x^{2} \operatorname{acos}{\left(x \right)}}{\left(1 - x^{2}\right)^{\frac{5}{2}}} + \frac{12 x \left(\frac{16 x^{8}}{\left(x^{4} - 1\right)^{2}} - \frac{12 x^{4}}{x^{4} - 1} + 1\right) \operatorname{acos}^{2}{\left(x \right)}}{x^{4} - 1} - \frac{3 x}{\left(x^{2} - 1\right)^{2}} + \frac{\operatorname{acos}{\left(x \right)}}{\left(1 - x^{2}\right)^{\frac{3}{2}}}\right)}{x^{4} - 1}$$
The graph