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How to use it?
- Derivative of:
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Derivative of (x^2+1)^3
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Derivative of ln(1-x)
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Derivative of sin(cosx)
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Derivative of (sin(x))^2+(cos(x))^2
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Identical expressions
- arcsin(sqrt(x^ two - one))/(cbrt(lnx)-(sinx)^ three)
- arc sinus of ( square root of (x squared minus 1)) divide by ( cubic root of (lnx) minus ( sinus of x) cubed )
- arc sinus of ( square root of (x to the power of two minus one)) divide by ( cubic root of (lnx) minus ( sinus of x) to the power of three)
- arcsin(√(x^2-1))/(cbrt(lnx)-(sinx)^3)
- arcsin(sqrt(x2-1))/(cbrt(lnx)-(sinx)3)
- arcsinsqrtx2-1/cbrtlnx-sinx3
- arcsin(sqrt(x²-1))/(cbrt(lnx)-(sinx)³)
- arcsin(sqrt(x to the power of 2-1))/(cbrt(lnx)-(sinx) to the power of 3)
- arcsinsqrtx^2-1/cbrtlnx-sinx^3
- arcsin(sqrt(x^2-1)) divide by (cbrt(lnx)-(sinx)^3)
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Similar expressions
- arcsin(sqrt(x^2+1))/(cbrt(lnx)-(sinx)^3)
- arcsin(sqrt(x^2-1))/(cbrt(lnx)+(sinx)^3)
Derivative of arcsin(sqrt(x^2-1))/(cbrt(lnx)-(sinx)^3)
The solution
You have entered
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/ ________\
| / 2 |
asin\\/ x - 1 /
--------------------
3 ________ 3
\/ log(x) - sin (x)
$$\frac{\operatorname{asin}{\left(\sqrt{x^{2} - 1} \right)}}{\sqrt[3]{\log{\left(x \right)}} - \sin^{3}{\left(x \right)}}$$
asin(sqrt(x^2 - 1))/(log(x)^(1/3) - sin(x)^3)
The first derivative
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/ ________\
/ 2 1 \ | / 2 |
|3*sin (x)*cos(x) - -------------|*asin\\/ x - 1 /
| 2/3 |
\ 3*x*log (x)/ x
---------------------------------------------------- + ----------------------------------------------
2 ________ ________
/3 ________ 3 \ / 2 / 2 /3 ________ 3 \
\\/ log(x) - sin (x)/ \/ 2 - x *\/ x - 1 *\\/ log(x) - sin (x)/
$$\frac{x}{\sqrt{2 - x^{2}} \sqrt{x^{2} - 1} \left(\sqrt[3]{\log{\left(x \right)}} - \sin^{3}{\left(x \right)}\right)} + \frac{\left(3 \sin^{2}{\left(x \right)} \cos{\left(x \right)} - \frac{1}{3 x \log{\left(x \right)}^{\frac{2}{3}}}\right) \operatorname{asin}{\left(\sqrt{x^{2} - 1} \right)}}{\left(\sqrt[3]{\log{\left(x \right)}} - \sin^{3}{\left(x \right)}\right)^{2}}$$
The second derivative
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/ 2 \
| / 1 2 \ |
| 2*|- ----------- + 9*sin (x)*cos(x)| |
2 2 | | 2/3 | | / _________\
x x | 3 2 \ x*log (x) / 3 2 | | / 2 | / 1 2 \
-1 + ------- + ------- |- 27*sin (x) + ------------ + ------------------------------------- + ------------ + 54*cos (x)*sin(x)|*asin\\/ -1 + x / 2*x*|- ----------- + 9*sin (x)*cos(x)|
2 2 | 2 5/3 3 ________ 3 2 2/3 | | 2/3 |
-1 + x -2 + x \ x *log (x) \/ log(x) - sin (x) x *log (x) / \ x*log (x) /
- ------------------------ + --------------------------------------------------------------------------------------------------------------------------- + -------------------------------------------------
_________ ________ /3 ________ 3 \ _________ ________
/ 2 / 2 9*\\/ log(x) - sin (x)/ / 2 / 2 /3 ________ 3 \
\/ -1 + x *\/ 2 - x 3*\/ -1 + x *\/ 2 - x *\\/ log(x) - sin (x)/
------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------
3 ________ 3
\/ log(x) - sin (x)
$$\frac{\frac{2 x \left(9 \sin^{2}{\left(x \right)} \cos{\left(x \right)} - \frac{1}{x \log{\left(x \right)}^{\frac{2}{3}}}\right)}{3 \sqrt{2 - x^{2}} \sqrt{x^{2} - 1} \left(\sqrt[3]{\log{\left(x \right)}} - \sin^{3}{\left(x \right)}\right)} + \frac{\left(\frac{2 \left(9 \sin^{2}{\left(x \right)} \cos{\left(x \right)} - \frac{1}{x \log{\left(x \right)}^{\frac{2}{3}}}\right)^{2}}{\sqrt[3]{\log{\left(x \right)}} - \sin^{3}{\left(x \right)}} - 27 \sin^{3}{\left(x \right)} + 54 \sin{\left(x \right)} \cos^{2}{\left(x \right)} + \frac{3}{x^{2} \log{\left(x \right)}^{\frac{2}{3}}} + \frac{2}{x^{2} \log{\left(x \right)}^{\frac{5}{3}}}\right) \operatorname{asin}{\left(\sqrt{x^{2} - 1} \right)}}{9 \left(\sqrt[3]{\log{\left(x \right)}} - \sin^{3}{\left(x \right)}\right)} - \frac{\frac{x^{2}}{x^{2} - 1} + \frac{x^{2}}{x^{2} - 2} - 1}{\sqrt{2 - x^{2}} \sqrt{x^{2} - 1}}}{\sqrt[3]{\log{\left(x \right)}} - \sin^{3}{\left(x \right)}}$$
The third derivative
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/ 3 \
| / 1 2 \ / 1 2 \ / 3 2 3 2 \| / 2 \
| 6*|- ----------- + 9*sin (x)*cos(x)| 6*|- ----------- + 9*sin (x)*cos(x)|*|- 27*sin (x) + ------------ + ------------ + 54*cos (x)*sin(x)|| | / 1 2 \ |
| | 2/3 | | 2/3 | | 2 5/3 2 2/3 || / _________\ / 2 2 2 \ | 2*|- ----------- + 9*sin (x)*cos(x)| |
| 3 \ x*log (x) / 10 18 18 2 \ x*log (x) / \ x *log (x) x *log (x) /| | / 2 | | 3 3 3*x 3*x 2*x | / 2 2 \ | | 2/3 | |
|- 162*cos (x) - ------------------------------------- + ------------ + ------------ + ------------ + 567*sin (x)*cos(x) - -----------------------------------------------------------------------------------------------------|*asin\\/ -1 + x / x*|- ------- - ------- + ---------- + ---------- + -------------------| / 1 2 \ | x x | | 3 2 \ x*log (x) / 3 2 |
| 2 3 8/3 3 5/3 3 2/3 3 ________ 3 | | 2 2 2 2 / 2\ / 2\| |- ----------- + 9*sin (x)*cos(x)|*|-1 + ------- + -------| x*|- 27*sin (x) + ------------ + ------------------------------------- + ------------ + 54*cos (x)*sin(x)|
| /3 ________ 3 \ x *log (x) x *log (x) x *log (x) \/ log(x) - sin (x) | | -1 + x -2 + x / 2\ / 2\ \-1 + x /*\-2 + x /| | 2/3 | | 2 2| | 2 5/3 3 ________ 3 2 2/3 |
\ \\/ log(x) - sin (x)/ / \ \-1 + x / \-2 + x / / \ x*log (x) / \ -1 + x -2 + x / \ x *log (x) \/ log(x) - sin (x) x *log (x) /
- ---------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------- + ----------------------------------------------------------------------- - ----------------------------------------------------------- + ----------------------------------------------------------------------------------------------------------
/3 ________ 3 \ _________ ________ _________ ________ _________ ________
27*\\/ log(x) - sin (x)/ / 2 / 2 / 2 / 2 /3 ________ 3 \ / 2 / 2 /3 ________ 3 \
\/ -1 + x *\/ 2 - x \/ -1 + x *\/ 2 - x *\\/ log(x) - sin (x)/ 3*\/ -1 + x *\/ 2 - x *\\/ log(x) - sin (x)/
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3 ________ 3
\/ log(x) - sin (x)
$$\frac{\frac{x \left(\frac{3 x^{2}}{\left(x^{2} - 1\right)^{2}} + \frac{2 x^{2}}{\left(x^{2} - 2\right) \left(x^{2} - 1\right)} + \frac{3 x^{2}}{\left(x^{2} - 2\right)^{2}} - \frac{3}{x^{2} - 1} - \frac{3}{x^{2} - 2}\right)}{\sqrt{2 - x^{2}} \sqrt{x^{2} - 1}} + \frac{x \left(\frac{2 \left(9 \sin^{2}{\left(x \right)} \cos{\left(x \right)} - \frac{1}{x \log{\left(x \right)}^{\frac{2}{3}}}\right)^{2}}{\sqrt[3]{\log{\left(x \right)}} - \sin^{3}{\left(x \right)}} - 27 \sin^{3}{\left(x \right)} + 54 \sin{\left(x \right)} \cos^{2}{\left(x \right)} + \frac{3}{x^{2} \log{\left(x \right)}^{\frac{2}{3}}} + \frac{2}{x^{2} \log{\left(x \right)}^{\frac{5}{3}}}\right)}{3 \sqrt{2 - x^{2}} \sqrt{x^{2} - 1} \left(\sqrt[3]{\log{\left(x \right)}} - \sin^{3}{\left(x \right)}\right)} - \frac{\left(- \frac{6 \left(9 \sin^{2}{\left(x \right)} \cos{\left(x \right)} - \frac{1}{x \log{\left(x \right)}^{\frac{2}{3}}}\right)^{3}}{\left(\sqrt[3]{\log{\left(x \right)}} - \sin^{3}{\left(x \right)}\right)^{2}} - \frac{6 \left(9 \sin^{2}{\left(x \right)} \cos{\left(x \right)} - \frac{1}{x \log{\left(x \right)}^{\frac{2}{3}}}\right) \left(- 27 \sin^{3}{\left(x \right)} + 54 \sin{\left(x \right)} \cos^{2}{\left(x \right)} + \frac{3}{x^{2} \log{\left(x \right)}^{\frac{2}{3}}} + \frac{2}{x^{2} \log{\left(x \right)}^{\frac{5}{3}}}\right)}{\sqrt[3]{\log{\left(x \right)}} - \sin^{3}{\left(x \right)}} + 567 \sin^{2}{\left(x \right)} \cos{\left(x \right)} - 162 \cos^{3}{\left(x \right)} + \frac{18}{x^{3} \log{\left(x \right)}^{\frac{2}{3}}} + \frac{18}{x^{3} \log{\left(x \right)}^{\frac{5}{3}}} + \frac{10}{x^{3} \log{\left(x \right)}^{\frac{8}{3}}}\right) \operatorname{asin}{\left(\sqrt{x^{2} - 1} \right)}}{27 \left(\sqrt[3]{\log{\left(x \right)}} - \sin^{3}{\left(x \right)}\right)} - \frac{\left(9 \sin^{2}{\left(x \right)} \cos{\left(x \right)} - \frac{1}{x \log{\left(x \right)}^{\frac{2}{3}}}\right) \left(\frac{x^{2}}{x^{2} - 1} + \frac{x^{2}}{x^{2} - 2} - 1\right)}{\sqrt{2 - x^{2}} \sqrt{x^{2} - 1} \left(\sqrt[3]{\log{\left(x \right)}} - \sin^{3}{\left(x \right)}\right)}}{\sqrt[3]{\log{\left(x \right)}} - \sin^{3}{\left(x \right)}}$$