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- Derivative of:
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Derivative of (x-3)^4
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Derivative of (x-7)^2
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Derivative of x^2+4
- Derivative of |x|/x
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Identical expressions
- log(log((x+ one)/(x- one), five), two)
- logarithm of ( logarithm of ((x plus 1) divide by (x minus 1),5),2)
- logarithm of ( logarithm of ((x plus one) divide by (x minus one), five), two)
- loglogx+1/x-1,5,2
- log(log((x+1) divide by (x-1),5),2)
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Similar expressions
- log(log((x-1)/(x-1),5),2)
- log(log((x+1)/(x+1),5),2)
Derivative of log(log((x+1)/(x-1),5),2)
The solution
You have entered
[src]
/ /x + 1 \ \ log|log|-----, 5|, 2| \ \x - 1 / /
$$\log{\left(\log{\left(\frac{x + 1}{x - 1} \right)} \right)}$$
log(log((x + 1)/(x - 1), 5), 2)
The first derivative
[src]
/ 1 x + 1 \
(x - 1)*|----- - --------|
|x - 1 2|
\ (x - 1) /
--------------------------
/x + 1 \
(x + 1)*log|-----, 5|
\x - 1 /
$$\frac{\left(x - 1\right) \left(\frac{1}{x - 1} - \frac{x + 1}{\left(x - 1\right)^{2}}\right)}{\left(x + 1\right) \log{\left(\frac{x + 1}{x - 1} \right)}}$$
The second derivative
[src]
/ / 1 + x \ \
| |1 - ------|*log(5)|
/ 1 + x \ | 1 1 \ -1 + x/ |
|1 - ------|*|- ----- - ------ - -------------------|*log(5)
\ -1 + x/ | 1 + x -1 + x /1 + x \|
| (1 + x)*log|------||
\ \-1 + x//
------------------------------------------------------------
/1 + x \
(1 + x)*log|------|
\-1 + x/
$$\frac{\left(1 - \frac{x + 1}{x - 1}\right) \left(- \frac{\left(1 - \frac{x + 1}{x - 1}\right) \log{\left(5 \right)}}{\left(x + 1\right) \log{\left(\frac{x + 1}{x - 1} \right)}} - \frac{1}{x + 1} - \frac{1}{x - 1}\right) \log{\left(5 \right)}}{\left(x + 1\right) \log{\left(\frac{x + 1}{x - 1} \right)}}$$
The third derivative
[src]
/ 2 \
| / 1 + x \ 2 / 1 + x \ / 1 + x \ |
| 2*|1 - ------| *log (5) 3*|1 - ------|*log(5) 3*|1 - ------|*log(5) |
/ 1 + x \ | 2 2 2 \ -1 + x/ \ -1 + x/ \ -1 + x/ |
|1 - ------|*|-------- + --------- + ---------------- + ----------------------- + --------------------- + ----------------------------|*log(5)
\ -1 + x/ | 2 2 (1 + x)*(-1 + x) 2 2/1 + x \ 2 /1 + x \ /1 + x \|
|(1 + x) (-1 + x) (1 + x) *log |------| (1 + x) *log|------| (1 + x)*(-1 + x)*log|------||
\ \-1 + x/ \-1 + x/ \-1 + x//
----------------------------------------------------------------------------------------------------------------------------------------------
/1 + x \
(1 + x)*log|------|
\-1 + x/
$$\frac{\left(1 - \frac{x + 1}{x - 1}\right) \left(\frac{2 \left(1 - \frac{x + 1}{x - 1}\right)^{2} \log{\left(5 \right)}^{2}}{\left(x + 1\right)^{2} \log{\left(\frac{x + 1}{x - 1} \right)}^{2}} + \frac{3 \left(1 - \frac{x + 1}{x - 1}\right) \log{\left(5 \right)}}{\left(x + 1\right)^{2} \log{\left(\frac{x + 1}{x - 1} \right)}} + \frac{3 \left(1 - \frac{x + 1}{x - 1}\right) \log{\left(5 \right)}}{\left(x - 1\right) \left(x + 1\right) \log{\left(\frac{x + 1}{x - 1} \right)}} + \frac{2}{\left(x + 1\right)^{2}} + \frac{2}{\left(x - 1\right) \left(x + 1\right)} + \frac{2}{\left(x - 1\right)^{2}}\right) \log{\left(5 \right)}}{\left(x + 1\right) \log{\left(\frac{x + 1}{x - 1} \right)}}$$