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- Derivative of a implicit defined function
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How to use it?
- Derivative of:
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Derivative of tanx
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Derivative of x^3-5x^2+x
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Derivative of sin2x+cos2x
- Derivative of ln((x^2+a)^0.5)
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Identical expressions
- arcsin((two /x^ three)^(one / two))
- arc sinus of ((2 divide by x cubed ) to the power of (1 divide by 2))
- arc sinus of ((two divide by x to the power of three) to the power of (one divide by two))
- arcsin((2/x3)(1/2))
- arcsin2/x31/2
- arcsin((2/x³)^(1/2))
- arcsin((2/x to the power of 3) to the power of (1/2))
- arcsin2/x^3^1/2
- arcsin((2 divide by x^3)^(1 divide by 2))
Derivative of arcsin((2/x^3)^(1/2))
The solution
You have entered
[src]
/ ____\
| / 2 |
asin| / -- |
| / 3 |
\\/ x /
$$\operatorname{asin}{\left(\sqrt{\frac{2}{x^{3}}} \right)}$$
asin(sqrt(2/x^3))
The first derivative
[src]
____
___ / 1
-3*\/ 2 * / --
/ 3
\/ x
------------------
________
/ 2
2*x* / 1 - --
/ 3
\/ x
$$- \frac{3 \sqrt{2} \sqrt{\frac{1}{x^{3}}}}{2 x \sqrt{1 - \frac{2}{x^{3}}}}$$
The second derivative
[src]
____
___ / 1 / 6 \
3*\/ 2 * / -- *|5 + -----------|
/ 3 | 3 / 2 \|
\/ x | x *|1 - --||
| | 3||
\ \ x //
-----------------------------------
________
2 / 2
4*x * / 1 - --
/ 3
\/ x
$$\frac{3 \sqrt{2} \left(5 + \frac{6}{x^{3} \left(1 - \frac{2}{x^{3}}\right)}\right) \sqrt{\frac{1}{x^{3}}}}{4 x^{2} \sqrt{1 - \frac{2}{x^{3}}}}$$
The third derivative
[src]
____
___ / 1 / 108 108 \
-3*\/ 2 * / -- *|35 + ------------ + -----------|
/ 3 | 2 3 / 2 \|
\/ x | 6 / 2 \ x *|1 - --||
| x *|1 - --| | 3||
| | 3| \ x /|
\ \ x / /
----------------------------------------------------
________
3 / 2
8*x * / 1 - --
/ 3
\/ x
$$- \frac{3 \sqrt{2} \left(35 + \frac{108}{x^{3} \left(1 - \frac{2}{x^{3}}\right)} + \frac{108}{x^{6} \left(1 - \frac{2}{x^{3}}\right)^{2}}\right) \sqrt{\frac{1}{x^{3}}}}{8 x^{3} \sqrt{1 - \frac{2}{x^{3}}}}$$