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How to use it?
- Derivative of:
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Derivative of (x^5+1)
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Derivative of x^(4/3)
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Derivative of (x^2)/36
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Derivative of x+log(x)
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Identical expressions
- log(one /(x- one),exp)
- logarithm of (1 divide by (x minus 1), exponent of )
- logarithm of (one divide by (x minus one), exponent of )
- log1/x-1,exp
- log(1 divide by (x-1),exp)
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Similar expressions
- log(1/(x+1),exp)
Derivative of log(1/(x-1),exp)
The solution
You have entered
[src]
/ 1 x\ log|-----, e | \x - 1 /
$$\log{\left(\frac{1}{x - 1} \right)}$$
log(1/(x - 1), exp(x))
The first derivative
[src]
/ / / 1 \\\|
| |log|-----||||
1 | d | \x - 1/||| x
- ----- + |-----|----------||| x*e
x - 1 \dxi_2\log(xi_2) //|xi_2=e
$$e^{x} \left. \frac{\partial}{\partial \xi_{2}} \frac{\log{\left(\frac{1}{x - 1} \right)}}{\log{\left(\xi_{2} \right)}} \right|_{\substack{ \xi_{2}=e^{x} }} - \frac{1}{x - 1}$$
The second derivative
[src]
1 / 2\ / 1 \ / / / 1 \\\|
------ + |1 + -|*log|------| | |log|------||||
1 -1 + x \ x/ \-1 + x/ | d | \-1 + x/||| x
--------- + ---------------------------- + |-----|-----------||| x*e
2 2 \dxi_2\ log(xi_2) //|xi_2=e
(-1 + x) x
$$e^{x} \left. \frac{\partial}{\partial \xi_{2}} \frac{\log{\left(\frac{1}{x - 1} \right)}}{\log{\left(\xi_{2} \right)}} \right|_{\substack{ \xi_{2}=e^{x} }} + \frac{1}{\left(x - 1\right)^{2}} + \frac{\left(1 + \frac{2}{x}\right) \log{\left(\frac{1}{x - 1} \right)} + \frac{1}{x - 1}}{x^{2}}$$
The third derivative
[src]
2 / 1 \ / 2\ / 1 \
1 + - 2*log|------| 2*|1 + -|*log|------|
1 1 x / 2\ / 1 \ 2 \-1 + x/ \ x/ \-1 + x/
/ / / 1 \\\| ------ + --------- + ------ + |1 + -|*log|------| + ---------- + ------------- + --------------------- / 1 / 2\ / 1 \\
| |log|------|||| -1 + x 2 -1 + x \ x/ \-1 + x/ x*(-1 + x) 2 x 2*|------ + |1 + -|*log|------||
2 | d | \-1 + x/||| x (-1 + x) x \-1 + x \ x/ \-1 + x//
- --------- + |-----|-----------||| x*e - ------------------------------------------------------------------------------------------------------ + --------------------------------
3 \dxi_2\ log(xi_2) //|xi_2=e 2 2
(-1 + x) x x
$$e^{x} \left. \frac{\partial}{\partial \xi_{2}} \frac{\log{\left(\frac{1}{x - 1} \right)}}{\log{\left(\xi_{2} \right)}} \right|_{\substack{ \xi_{2}=e^{x} }} - \frac{2}{\left(x - 1\right)^{3}} + \frac{2 \left(\left(1 + \frac{2}{x}\right) \log{\left(\frac{1}{x - 1} \right)} + \frac{1}{x - 1}\right)}{x^{2}} - \frac{\left(1 + \frac{2}{x}\right) \log{\left(\frac{1}{x - 1} \right)} + \frac{1 + \frac{2}{x}}{x - 1} + \frac{1}{x - 1} + \frac{1}{\left(x - 1\right)^{2}} + \frac{2 \left(1 + \frac{2}{x}\right) \log{\left(\frac{1}{x - 1} \right)}}{x} + \frac{2}{x \left(x - 1\right)} + \frac{2 \log{\left(\frac{1}{x - 1} \right)}}{x^{2}}}{x^{2}}$$