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How to use it?
- Derivative of:
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Derivative of tanx
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Derivative of y=3x-2
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Derivative of y=(sqrt(x+1))^1/4*cos(3x)
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Derivative of y=cosx/x
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Identical expressions
- arccos(x)/(x^ three - one)
- arc co sinus of e of (x) divide by (x cubed minus 1)
- arc co sinus of e of (x) divide by (x to the power of three minus one)
- arccos(x)/(x3-1)
- arccosx/x3-1
- arccos(x)/(x³-1)
- arccos(x)/(x to the power of 3-1)
- arccosx/x^3-1
- arccos(x) divide by (x^3-1)
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Similar expressions
- arccos(x)/(x^3+1)
- arccosx/(x^3-1)
Derivative of arccos(x)/(x^3-1)
The solution
You have entered
[src]
acos(x) ------- 3 x - 1
$$\frac{\operatorname{acos}{\left(x \right)}}{x^{3} - 1}$$
acos(x)/(x^3 - 1)
The first derivative
[src]
2
1 3*x *acos(x)
- -------------------- - ------------
________ 2
/ 2 / 3 \ / 3 \
\/ 1 - x *\x - 1/ \x - 1/
$$- \frac{3 x^{2} \operatorname{acos}{\left(x \right)}}{\left(x^{3} - 1\right)^{2}} - \frac{1}{\sqrt{1 - x^{2}} \left(x^{3} - 1\right)}$$
The second derivative
[src]
/ / 3 \ \
| | 3*x | |
| 6*|-1 + -------|*acos(x)|
| | 3| |
| 1 6*x \ -1 + x / |
x*|- ----------- + --------------------- + ------------------------|
| 3/2 ________ 3 |
| / 2\ / 2 / 3\ -1 + x |
\ \1 - x / \/ 1 - x *\-1 + x / /
--------------------------------------------------------------------
3
-1 + x
$$\frac{x \left(\frac{6 x}{\sqrt{1 - x^{2}} \left(x^{3} - 1\right)} + \frac{6 \left(\frac{3 x^{3}}{x^{3} - 1} - 1\right) \operatorname{acos}{\left(x \right)}}{x^{3} - 1} - \frac{1}{\left(1 - x^{2}\right)^{\frac{3}{2}}}\right)}{x^{3} - 1}$$
The third derivative
[src]
/ 3 6 \
2 | 18*x 27*x | / 3 \
3*x 6*|1 - ------- + ----------|*acos(x) | 3*x |
-1 + ------- | 3 2| 18*x*|-1 + -------|
2 | -1 + x / 3\ | 3 | 3|
-1 + x \ \-1 + x / / 9*x \ -1 + x /
------------ - ------------------------------------ + --------------------- - ---------------------
3/2 3 3/2 ________
/ 2\ -1 + x / 2\ / 3\ / 2 / 3\
\1 - x / \1 - x / *\-1 + x / \/ 1 - x *\-1 + x /
---------------------------------------------------------------------------------------------------
3
-1 + x
$$\frac{\frac{9 x^{3}}{\left(1 - x^{2}\right)^{\frac{3}{2}} \left(x^{3} - 1\right)} - \frac{18 x \left(\frac{3 x^{3}}{x^{3} - 1} - 1\right)}{\sqrt{1 - x^{2}} \left(x^{3} - 1\right)} - \frac{6 \left(\frac{27 x^{6}}{\left(x^{3} - 1\right)^{2}} - \frac{18 x^{3}}{x^{3} - 1} + 1\right) \operatorname{acos}{\left(x \right)}}{x^{3} - 1} + \frac{\frac{3 x^{2}}{x^{2} - 1} - 1}{\left(1 - x^{2}\right)^{\frac{3}{2}}}}{x^{3} - 1}$$