Mister Exam
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How to use it?
- Derivative of:
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Derivative of cos(x)/e^x
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Derivative of acos(1/x)
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Identical expressions
- (ln(ln(x)))^(ln(x))^(- one)
- (ln(ln(x))) to the power of (ln(x)) to the power of ( minus 1)
- (ln(ln(x))) to the power of (ln(x)) to the power of ( minus one)
- (ln(ln(x)))(ln(x))(-1)
- lnlnxlnx-1
- lnlnx^lnx^-1
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Similar expressions
- (ln(ln(x)))^(ln(x))^(1)
Derivative of (ln(ln(x)))^(ln(x))^(-1)
The solution
You have entered
[src]
1
------
log(x)
(log(log(x)))
$$\log{\left(\log{\left(x \right)} \right)}^{\frac{1}{\log{\left(x \right)}}}$$
log(log(x))^(1/log(x))
Detail solution
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Don't know the steps in finding this derivative.
But the derivative is
The answer is:
The first derivative
[src]
1
------
log(x) / 1 log(log(log(x)))\
(log(log(x))) *|--------------------- - ----------------|
| 2 2 |
\x*log (x)*log(log(x)) x*log (x) /
$$\left(- \frac{\log{\left(\log{\left(\log{\left(x \right)} \right)} \right)}}{x \log{\left(x \right)}^{2}} + \frac{1}{x \log{\left(x \right)}^{2} \log{\left(\log{\left(x \right)} \right)}}\right) \log{\left(\log{\left(x \right)} \right)}^{\frac{1}{\log{\left(x \right)}}}$$
The second derivative
[src]
/ 2 \
1 | / 1 \ |
------ | |- ----------- + log(log(log(x)))| |
log(x) | 1 \ log(log(x)) / 1 3 2*log(log(log(x))) |
(log(log(x))) *|- ----------- + ----------------------------------- - ------------------- - ------------------ + ------------------ + log(log(log(x)))|
| log(log(x)) 2 2 log(x)*log(log(x)) log(x) |
\ log (x) log(x)*log (log(x)) /
------------------------------------------------------------------------------------------------------------------------------------------------------------
2 2
x *log (x)
$$\frac{\left(\frac{\left(\log{\left(\log{\left(\log{\left(x \right)} \right)} \right)} - \frac{1}{\log{\left(\log{\left(x \right)} \right)}}\right)^{2}}{\log{\left(x \right)}^{2}} + \log{\left(\log{\left(\log{\left(x \right)} \right)} \right)} - \frac{1}{\log{\left(\log{\left(x \right)} \right)}} + \frac{2 \log{\left(\log{\left(\log{\left(x \right)} \right)} \right)}}{\log{\left(x \right)}} - \frac{3}{\log{\left(x \right)} \log{\left(\log{\left(x \right)} \right)}} - \frac{1}{\log{\left(x \right)} \log{\left(\log{\left(x \right)} \right)}^{2}}\right) \log{\left(\log{\left(x \right)} \right)}^{\frac{1}{\log{\left(x \right)}}}}{x^{2} \log{\left(x \right)}^{2}}$$
The third derivative
[src]
/ 3 / 1 \ / 1 1 2*log(log(log(x))) 3 \\
1 | / 1 \ 3*|- ----------- + log(log(log(x)))|*|----------- - log(log(log(x))) + ------------------- - ------------------ + ------------------||
------ | |- ----------- + log(log(log(x)))| \ log(log(x)) / |log(log(x)) 2 log(x) log(x)*log(log(x))||
log(x) | 2 \ log(log(x)) / 6*log(log(log(x))) 6*log(log(log(x))) 2 3 6 9 11 \ log(x)*log (log(x)) /|
(log(log(x))) *|-2*log(log(log(x))) + ----------- - ----------------------------------- - ------------------ - ------------------ + -------------------- + ------------------- + -------------------- + ------------------ + ------------------- + -------------------------------------------------------------------------------------------------------------------------------------|
| log(log(x)) 4 log(x) 2 2 3 2 2 2 log(x)*log(log(x)) 2 2 |
\ log (x) log (x) log (x)*log (log(x)) log(x)*log (log(x)) log (x)*log (log(x)) log (x)*log(log(x)) log (x) /
----------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------
3 2
x *log (x)
$$\frac{\left(- \frac{\left(\log{\left(\log{\left(\log{\left(x \right)} \right)} \right)} - \frac{1}{\log{\left(\log{\left(x \right)} \right)}}\right)^{3}}{\log{\left(x \right)}^{4}} + \frac{3 \left(\log{\left(\log{\left(\log{\left(x \right)} \right)} \right)} - \frac{1}{\log{\left(\log{\left(x \right)} \right)}}\right) \left(- \log{\left(\log{\left(\log{\left(x \right)} \right)} \right)} + \frac{1}{\log{\left(\log{\left(x \right)} \right)}} - \frac{2 \log{\left(\log{\left(\log{\left(x \right)} \right)} \right)}}{\log{\left(x \right)}} + \frac{3}{\log{\left(x \right)} \log{\left(\log{\left(x \right)} \right)}} + \frac{1}{\log{\left(x \right)} \log{\left(\log{\left(x \right)} \right)}^{2}}\right)}{\log{\left(x \right)}^{2}} - 2 \log{\left(\log{\left(\log{\left(x \right)} \right)} \right)} + \frac{2}{\log{\left(\log{\left(x \right)} \right)}} - \frac{6 \log{\left(\log{\left(\log{\left(x \right)} \right)} \right)}}{\log{\left(x \right)}} + \frac{9}{\log{\left(x \right)} \log{\left(\log{\left(x \right)} \right)}} + \frac{3}{\log{\left(x \right)} \log{\left(\log{\left(x \right)} \right)}^{2}} - \frac{6 \log{\left(\log{\left(\log{\left(x \right)} \right)} \right)}}{\log{\left(x \right)}^{2}} + \frac{11}{\log{\left(x \right)}^{2} \log{\left(\log{\left(x \right)} \right)}} + \frac{6}{\log{\left(x \right)}^{2} \log{\left(\log{\left(x \right)} \right)}^{2}} + \frac{2}{\log{\left(x \right)}^{2} \log{\left(\log{\left(x \right)} \right)}^{3}}\right) \log{\left(\log{\left(x \right)} \right)}^{\frac{1}{\log{\left(x \right)}}}}{x^{3} \log{\left(x \right)}^{2}}$$