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How to use it?
- Derivative of:
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Derivative of (x+5)/(x+1)
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Derivative of tan(x/2)-cot(x/2)
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Derivative of sqrt(x^3-1)
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Derivative of sin(x)*cos(x)+x
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Identical expressions
- arcsin(log(x)/log(three))^(one / five)
- arc sinus of ( logarithm of (x) divide by logarithm of (3)) to the power of (1 divide by 5)
- arc sinus of ( logarithm of (x) divide by logarithm of (three)) to the power of (one divide by five)
- arcsin(log(x)/log(3))(1/5)
- arcsinlogx/log31/5
- arcsinlogx/log3^1/5
- arcsin(log(x) divide by log(3))^(1 divide by 5)
Derivative of arcsin(log(x)/log(3))^(1/5)
The solution
You have entered
[src]
______________ / /log(x)\ 5 / asin|------| \/ \log(3)/
$$\sqrt[5]{\operatorname{asin}{\left(\frac{\log{\left(x \right)}}{\log{\left(3 \right)}} \right)}}$$
asin(log(x)/log(3))^(1/5)
The first derivative
[src]
1
----------------------------------------------
_____________
/ 2
/ log (x) 4/5/log(x)\
5*x* / 1 - ------- *asin |------|*log(3)
/ 2 \log(3)/
\/ log (3)
$$\frac{1}{5 x \sqrt{- \frac{\log{\left(x \right)}^{2}}{\log{\left(3 \right)}^{2}} + 1} \log{\left(3 \right)} \operatorname{asin}^{\frac{4}{5}}{\left(\frac{\log{\left(x \right)}}{\log{\left(3 \right)}} \right)}}$$
The second derivative
[src]
5 4 5*log(x)
- ------------------- + ---------------------------------- + ------------------------
_____________ / 2 \ 3/2
/ 2 | log (x)| /log(x)\ / 2 \
/ log (x) |-1 + -------|*asin|------|*log(3) | log (x)| 2
/ 1 - ------- | 2 | \log(3)/ |1 - -------| *log (3)
/ 2 \ log (3)/ | 2 |
\/ log (3) \ log (3)/
-------------------------------------------------------------------------------------
2 4/5/log(x)\
25*x *asin |------|*log(3)
\log(3)/
$$\frac{\frac{4}{\left(\frac{\log{\left(x \right)}^{2}}{\log{\left(3 \right)}^{2}} - 1\right) \log{\left(3 \right)} \operatorname{asin}{\left(\frac{\log{\left(x \right)}}{\log{\left(3 \right)}} \right)}} - \frac{5}{\sqrt{- \frac{\log{\left(x \right)}^{2}}{\log{\left(3 \right)}^{2}} + 1}} + \frac{5 \log{\left(x \right)}}{\left(- \frac{\log{\left(x \right)}^{2}}{\log{\left(3 \right)}^{2}} + 1\right)^{\frac{3}{2}} \log{\left(3 \right)}^{2}}}{25 x^{2} \log{\left(3 \right)} \operatorname{asin}^{\frac{4}{5}}{\left(\frac{\log{\left(x \right)}}{\log{\left(3 \right)}} \right)}}$$
The third derivative
[src]
2
50 25 75*log(x) 60 36 75*log (x) 60*log(x)
------------------- + ------------------------ - ------------------------ - ---------------------------------- + -------------------------------------- + ------------------------ - ------------------------------------
_____________ 3/2 3/2 / 2 \ 3/2 5/2 2
/ 2 / 2 \ / 2 \ | log (x)| /log(x)\ / 2 \ / 2 \ / 2 \
/ log (x) | log (x)| 2 | log (x)| 2 |-1 + -------|*asin|------|*log(3) | log (x)| 2/log(x)\ 2 | log (x)| 4 | log (x)| /log(x)\ 3
/ 1 - ------- |1 - -------| *log (3) |1 - -------| *log (3) | 2 | \log(3)/ |1 - -------| *asin |------|*log (3) |1 - -------| *log (3) |-1 + -------| *asin|------|*log (3)
/ 2 | 2 | | 2 | \ log (3)/ | 2 | \log(3)/ | 2 | | 2 | \log(3)/
\/ log (3) \ log (3)/ \ log (3)/ \ log (3)/ \ log (3)/ \ log (3)/
-------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------
3 4/5/log(x)\
125*x *asin |------|*log(3)
\log(3)/
$$\frac{- \frac{60}{\left(\frac{\log{\left(x \right)}^{2}}{\log{\left(3 \right)}^{2}} - 1\right) \log{\left(3 \right)} \operatorname{asin}{\left(\frac{\log{\left(x \right)}}{\log{\left(3 \right)}} \right)}} - \frac{60 \log{\left(x \right)}}{\left(\frac{\log{\left(x \right)}^{2}}{\log{\left(3 \right)}^{2}} - 1\right)^{2} \log{\left(3 \right)}^{3} \operatorname{asin}{\left(\frac{\log{\left(x \right)}}{\log{\left(3 \right)}} \right)}} + \frac{50}{\sqrt{- \frac{\log{\left(x \right)}^{2}}{\log{\left(3 \right)}^{2}} + 1}} - \frac{75 \log{\left(x \right)}}{\left(- \frac{\log{\left(x \right)}^{2}}{\log{\left(3 \right)}^{2}} + 1\right)^{\frac{3}{2}} \log{\left(3 \right)}^{2}} + \frac{25}{\left(- \frac{\log{\left(x \right)}^{2}}{\log{\left(3 \right)}^{2}} + 1\right)^{\frac{3}{2}} \log{\left(3 \right)}^{2}} + \frac{36}{\left(- \frac{\log{\left(x \right)}^{2}}{\log{\left(3 \right)}^{2}} + 1\right)^{\frac{3}{2}} \log{\left(3 \right)}^{2} \operatorname{asin}^{2}{\left(\frac{\log{\left(x \right)}}{\log{\left(3 \right)}} \right)}} + \frac{75 \log{\left(x \right)}^{2}}{\left(- \frac{\log{\left(x \right)}^{2}}{\log{\left(3 \right)}^{2}} + 1\right)^{\frac{5}{2}} \log{\left(3 \right)}^{4}}}{125 x^{3} \log{\left(3 \right)} \operatorname{asin}^{\frac{4}{5}}{\left(\frac{\log{\left(x \right)}}{\log{\left(3 \right)}} \right)}}$$