Mister Exam
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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^-2
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Derivative of x+3
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Derivative of (-1)/x^2
- Derivative of e^x^3
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Identical expressions
- y=(ln(arctg(three /x)))^(- one)
- y equally (ln(arctg(3 divide by x))) to the power of ( minus 1)
- y equally (ln(arctg(three divide by x))) to the power of ( minus one)
- y=(ln(arctg(3/x)))(-1)
- y=lnarctg3/x-1
- y=lnarctg3/x^-1
- y=(ln(arctg(3 divide by x)))^(-1)
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Similar expressions
- y=(ln(arctg(3/x)))^(1)
Derivative of y=(ln(arctg(3/x)))^(-1)
The solution
You have entered
[src]
1 ------------ / /3\\ log|atan|-|| \ \x//
$$\frac{1}{\log{\left(\operatorname{atan}{\left(\frac{3}{x} \right)} \right)}}$$
1/log(atan(3/x))
The first derivative
[src]
3 --------------------------------- 2 / 9 \ /3\ 2/ /3\\ x *|1 + --|*atan|-|*log |atan|-|| | 2| \x/ \ \x// \ x /
$$\frac{3}{x^{2} \left(1 + \frac{9}{x^{2}}\right) \log{\left(\operatorname{atan}{\left(\frac{3}{x} \right)} \right)}^{2} \operatorname{atan}{\left(\frac{3}{x} \right)}}$$
The second derivative
[src]
/ 18 3 6 \
3*|-2 + ----------- + ------------------ + -------------------------------|
| 2 / 9 \ / 9 \ /3\ / 9 \ /3\ / /3\\|
| x *|1 + --| x*|1 + --|*atan|-| x*|1 + --|*atan|-|*log|atan|-|||
| | 2| | 2| \x/ | 2| \x/ \ \x//|
\ \ x / \ x / \ x / /
---------------------------------------------------------------------------
3 / 9 \ /3\ 2/ /3\\
x *|1 + --|*atan|-|*log |atan|-||
| 2| \x/ \ \x//
\ x /
$$\frac{3 \left(-2 + \frac{3}{x \left(1 + \frac{9}{x^{2}}\right) \operatorname{atan}{\left(\frac{3}{x} \right)}} + \frac{6}{x \left(1 + \frac{9}{x^{2}}\right) \log{\left(\operatorname{atan}{\left(\frac{3}{x} \right)} \right)} \operatorname{atan}{\left(\frac{3}{x} \right)}} + \frac{18}{x^{2} \left(1 + \frac{9}{x^{2}}\right)}\right)}{x^{3} \left(1 + \frac{9}{x^{2}}\right) \log{\left(\operatorname{atan}{\left(\frac{3}{x} \right)} \right)}^{2} \operatorname{atan}{\left(\frac{3}{x} \right)}}$$
The third derivative
[src]
/ 21 108 3 3 27 6 9 9 54 \
18*|1 - ----------- + ------------ - ------------------ + --------------------- + -------------------- - ------------------------------- + ---------------------------------- + ----------------------------------- + ---------------------------------|
| 2 / 9 \ 2 / 9 \ /3\ 2 2 / 9 \ /3\ / /3\\ 2 2 2 |
| x *|1 + --| 4 / 9 \ x*|1 + --|*atan|-| 2 / 9 \ 2/3\ 3 / 9 \ /3\ x*|1 + --|*atan|-|*log|atan|-|| 2 / 9 \ 2/3\ / /3\\ 2 / 9 \ 2/3\ 2/ /3\\ 3 / 9 \ /3\ / /3\\|
| | 2| x *|1 + --| | 2| \x/ x *|1 + --| *atan |-| x *|1 + --| *atan|-| | 2| \x/ \ \x// x *|1 + --| *atan |-|*log|atan|-|| x *|1 + --| *atan |-|*log |atan|-|| x *|1 + --| *atan|-|*log|atan|-|||
| \ x / | 2| \ x / | 2| \x/ | 2| \x/ \ x / | 2| \x/ \ \x// | 2| \x/ \ \x// | 2| \x/ \ \x//|
\ \ x / \ x / \ x / \ x / \ x / \ x / /
--------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------
4 / 9 \ /3\ 2/ /3\\
x *|1 + --|*atan|-|*log |atan|-||
| 2| \x/ \ \x//
\ x /
$$\frac{18 \left(1 - \frac{3}{x \left(1 + \frac{9}{x^{2}}\right) \operatorname{atan}{\left(\frac{3}{x} \right)}} - \frac{6}{x \left(1 + \frac{9}{x^{2}}\right) \log{\left(\operatorname{atan}{\left(\frac{3}{x} \right)} \right)} \operatorname{atan}{\left(\frac{3}{x} \right)}} - \frac{21}{x^{2} \left(1 + \frac{9}{x^{2}}\right)} + \frac{3}{x^{2} \left(1 + \frac{9}{x^{2}}\right)^{2} \operatorname{atan}^{2}{\left(\frac{3}{x} \right)}} + \frac{9}{x^{2} \left(1 + \frac{9}{x^{2}}\right)^{2} \log{\left(\operatorname{atan}{\left(\frac{3}{x} \right)} \right)} \operatorname{atan}^{2}{\left(\frac{3}{x} \right)}} + \frac{9}{x^{2} \left(1 + \frac{9}{x^{2}}\right)^{2} \log{\left(\operatorname{atan}{\left(\frac{3}{x} \right)} \right)}^{2} \operatorname{atan}^{2}{\left(\frac{3}{x} \right)}} + \frac{27}{x^{3} \left(1 + \frac{9}{x^{2}}\right)^{2} \operatorname{atan}{\left(\frac{3}{x} \right)}} + \frac{54}{x^{3} \left(1 + \frac{9}{x^{2}}\right)^{2} \log{\left(\operatorname{atan}{\left(\frac{3}{x} \right)} \right)} \operatorname{atan}{\left(\frac{3}{x} \right)}} + \frac{108}{x^{4} \left(1 + \frac{9}{x^{2}}\right)^{2}}\right)}{x^{4} \left(1 + \frac{9}{x^{2}}\right) \log{\left(\operatorname{atan}{\left(\frac{3}{x} \right)} \right)}^{2} \operatorname{atan}{\left(\frac{3}{x} \right)}}$$
The graph