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How to use it?
- Derivative of:
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Derivative of f(x)=2x⁴
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Derivative of arctg((tgx-ctgx)/sqrt(2))
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Derivative of sin(2πx)
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Derivative of 1/sqrt(1-2x)
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Identical expressions
- x*arctg(x)-ln((one +x^ two))^ two
- x multiply by arctg(x) minus ln((1 plus x squared )) squared
- x multiply by arctg(x) minus ln((one plus x to the power of two)) to the power of two
- x*arctg(x)-ln((1+x2))2
- x*arctgx-ln1+x22
- x*arctg(x)-ln((1+x²))²
- x*arctg(x)-ln((1+x to the power of 2)) to the power of 2
- xarctg(x)-ln((1+x^2))^2
- xarctg(x)-ln((1+x2))2
- xarctgx-ln1+x22
- xarctgx-ln1+x^2^2
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Similar expressions
- x*arctg(x)-ln((1-x^2))^2
- x*arctg(x)+ln((1+x^2))^2
Derivative of x*arctg(x)-ln((1+x^2))^2
The solution
You have entered
[src]
2/ 2\ x*atan(x) - log \1 + x /
$$x \operatorname{atan}{\left(x \right)} - \log{\left(x^{2} + 1 \right)}^{2}$$
x*atan(x) - log(1 + x^2)^2
The first derivative
[src]
/ 2\
x 4*x*log\1 + x /
------ - --------------- + atan(x)
2 2
1 + x 1 + x
$$- \frac{4 x \log{\left(x^{2} + 1 \right)}}{x^{2} + 1} + \frac{x}{x^{2} + 1} + \operatorname{atan}{\left(x \right)}$$
The second derivative
[src]
/ 2 2 / 2\\
| / 2\ 5*x 4*x *log\1 + x /|
2*|1 - 2*log\1 + x / - ------ + ----------------|
| 2 2 |
\ 1 + x 1 + x /
-------------------------------------------------
2
1 + x
$$\frac{2 \left(\frac{4 x^{2} \log{\left(x^{2} + 1 \right)}}{x^{2} + 1} - \frac{5 x^{2}}{x^{2} + 1} - 2 \log{\left(x^{2} + 1 \right)} + 1\right)}{x^{2} + 1}$$
The third derivative
[src]
/ 2 2 / 2\\
| / 2\ 7*x 4*x *log\1 + x /|
8*x*|-4 + 3*log\1 + x / + ------ - ----------------|
| 2 2 |
\ 1 + x 1 + x /
----------------------------------------------------
2
/ 2\
\1 + x /
$$\frac{8 x \left(- \frac{4 x^{2} \log{\left(x^{2} + 1 \right)}}{x^{2} + 1} + \frac{7 x^{2}}{x^{2} + 1} + 3 \log{\left(x^{2} + 1 \right)} - 4\right)}{\left(x^{2} + 1\right)^{2}}$$