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- Derivative of a implicit defined function
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How to use it?
- Derivative of:
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Derivative of (x^3-1)(x^2+x+1)
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Derivative of y/2
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Derivative of (x+5)/(x-1)
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Derivative of x+9
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Identical expressions
- arcctg(sqrt(x))/ln(x+ one)
- arcctg( square root of (x)) divide by ln(x plus 1)
- arcctg( square root of (x)) divide by ln(x plus one)
- arcctg(√(x))/ln(x+1)
- arcctgsqrtx/lnx+1
- arcctg(sqrt(x)) divide by ln(x+1)
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Similar expressions
- arcctg(sqrt(x))/ln(x-1)
- arcctg(sqrt(x))/lnx+1
Derivative of arcctg(sqrt(x))/ln(x+1)
The solution
You have entered
[src]
/ ___\ acot\\/ x / ----------- log(x + 1)
$$\frac{\operatorname{acot}{\left(\sqrt{x} \right)}}{\log{\left(x + 1 \right)}}$$
acot(sqrt(x))/log(x + 1)
The first derivative
[src]
/ ___\
acot\\/ x / 1
- ------------------- - --------------------------
2 ___
(x + 1)*log (x + 1) 2*\/ x *(1 + x)*log(x + 1)
$$- \frac{\operatorname{acot}{\left(\sqrt{x} \right)}}{\left(x + 1\right) \log{\left(x + 1 \right)}^{2}} - \frac{1}{2 \sqrt{x} \left(x + 1\right) \log{\left(x + 1 \right)}}$$
The second derivative
[src]
1 2 / 2 \ / ___\
- + ----- |1 + ----------|*acot\\/ x /
x 1 + x 1 \ log(1 + x)/
--------- + ------------------------ + ----------------------------
___ ___ (1 + x)*log(1 + x)
4*\/ x \/ x *(1 + x)*log(1 + x)
-------------------------------------------------------------------
(1 + x)*log(1 + x)
$$\frac{\frac{\left(1 + \frac{2}{\log{\left(x + 1 \right)}}\right) \operatorname{acot}{\left(\sqrt{x} \right)}}{\left(x + 1\right) \log{\left(x + 1 \right)}} + \frac{\frac{2}{x + 1} + \frac{1}{x}}{4 \sqrt{x}} + \frac{1}{\sqrt{x} \left(x + 1\right) \log{\left(x + 1 \right)}}}{\left(x + 1\right) \log{\left(x + 1 \right)}}$$
The third derivative
[src]
/3 8 4 / 3 3 \ / ___\ \
|-- + -------- + --------- 2*|1 + ---------- + -----------|*acot\\/ x / / 2 \ /1 2 \ |
| 2 2 x*(1 + x) | log(1 + x) 2 | 3*|1 + ----------| 3*|- + -----| |
|x (1 + x) \ log (1 + x)/ \ log(1 + x)/ \x 1 + x/ |
-|------------------------- + -------------------------------------------- + --------------------------- + --------------------------|
| ___ 2 ___ 2 ___ |
\ 8*\/ x (1 + x) *log(1 + x) 2*\/ x *(1 + x) *log(1 + x) 4*\/ x *(1 + x)*log(1 + x)/
---------------------------------------------------------------------------------------------------------------------------------------
(1 + x)*log(1 + x)
$$- \frac{\frac{2 \left(1 + \frac{3}{\log{\left(x + 1 \right)}} + \frac{3}{\log{\left(x + 1 \right)}^{2}}\right) \operatorname{acot}{\left(\sqrt{x} \right)}}{\left(x + 1\right)^{2} \log{\left(x + 1 \right)}} + \frac{3 \left(1 + \frac{2}{\log{\left(x + 1 \right)}}\right)}{2 \sqrt{x} \left(x + 1\right)^{2} \log{\left(x + 1 \right)}} + \frac{\frac{8}{\left(x + 1\right)^{2}} + \frac{4}{x \left(x + 1\right)} + \frac{3}{x^{2}}}{8 \sqrt{x}} + \frac{3 \left(\frac{2}{x + 1} + \frac{1}{x}\right)}{4 \sqrt{x} \left(x + 1\right) \log{\left(x + 1 \right)}}}{\left(x + 1\right) \log{\left(x + 1 \right)}}$$