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- Derivative of:
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Derivative of (x^2+1)^3
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Derivative of sin(cosx)
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Derivative of ln(-x)
- Derivative of i*n*sin(x)
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Identical expressions
- arccos(x- three *ln(one +x^ two))
- arc co sinus of e of (x minus 3 multiply by ln(1 plus x squared ))
- arc co sinus of e of (x minus three multiply by ln(one plus x to the power of two))
- arccos(x-3*ln(1+x2))
- arccosx-3*ln1+x2
- arccos(x-3*ln(1+x²))
- arccos(x-3*ln(1+x to the power of 2))
- arccos(x-3ln(1+x^2))
- arccos(x-3ln(1+x2))
- arccosx-3ln1+x2
- arccosx-3ln1+x^2
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Similar expressions
- arccos(x-3*ln(1-x^2))
- arccos(x+3*ln(1+x^2))
Derivative of arccos(x-3*ln(1+x^2))
The solution
You have entered
[src]
/ / 2\\ acos\x - 3*log\1 + x //
$$\operatorname{acos}{\left(x - 3 \log{\left(x^{2} + 1 \right)} \right)}$$
acos(x - 3*log(1 + x^2))
The first derivative
[src]
/ 6*x \
-|1 - ------|
| 2|
\ 1 + x /
------------------------------
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/ 2
/ / / 2\\
\/ 1 - \x - 3*log\1 + x //
$$- \frac{- \frac{6 x}{x^{2} + 1} + 1}{\sqrt{1 - \left(x - 3 \log{\left(x^{2} + 1 \right)}\right)^{2}}}$$
The second derivative
[src]
/ / 2 \ 2 \
| | 2*x | / 6*x \ / / 2\\|
|6*|-1 + ------| |-1 + ------| *\x - 3*log\1 + x //|
| | 2| | 2| |
| \ 1 + x / \ 1 + x / |
-|--------------- + ----------------------------------|
| 2 2 |
| 1 + x / / 2\\ |
\ 1 - \x - 3*log\1 + x // /
--------------------------------------------------------
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/ 2
/ / / 2\\
\/ 1 - \x - 3*log\1 + x //
$$- \frac{\frac{6 \left(\frac{2 x^{2}}{x^{2} + 1} - 1\right)}{x^{2} + 1} + \frac{\left(x - 3 \log{\left(x^{2} + 1 \right)}\right) \left(\frac{6 x}{x^{2} + 1} - 1\right)^{2}}{1 - \left(x - 3 \log{\left(x^{2} + 1 \right)}\right)^{2}}}{\sqrt{1 - \left(x - 3 \log{\left(x^{2} + 1 \right)}\right)^{2}}}$$
The third derivative
[src]
3 3 2 / 2 \ / 2 \
/ 6*x \ / 6*x \ / / 2\\ | 4*x | | 2*x | / 6*x \ / / 2\\
|-1 + ------| 3*|-1 + ------| *\x - 3*log\1 + x // 12*x*|-3 + ------| 18*|-1 + ------|*|-1 + ------|*\x - 3*log\1 + x //
| 2| | 2| | 2| | 2| | 2|
\ 1 + x / \ 1 + x / \ 1 + x / \ 1 + x / \ 1 + x /
------------------------ + ------------------------------------- + ------------------ + --------------------------------------------------
2 2 2 / 2\
/ / 2\\ / 2\ / 2\ / 2\ | / / 2\\ |
1 - \x - 3*log\1 + x // | / / 2\\ | \1 + x / \1 + x /*\1 - \x - 3*log\1 + x // /
\1 - \x - 3*log\1 + x // /
------------------------------------------------------------------------------------------------------------------------------------------
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/ 2
/ / / 2\\
\/ 1 - \x - 3*log\1 + x //
$$\frac{\frac{12 x \left(\frac{4 x^{2}}{x^{2} + 1} - 3\right)}{\left(x^{2} + 1\right)^{2}} + \frac{18 \left(x - 3 \log{\left(x^{2} + 1 \right)}\right) \left(\frac{6 x}{x^{2} + 1} - 1\right) \left(\frac{2 x^{2}}{x^{2} + 1} - 1\right)}{\left(1 - \left(x - 3 \log{\left(x^{2} + 1 \right)}\right)^{2}\right) \left(x^{2} + 1\right)} + \frac{\left(\frac{6 x}{x^{2} + 1} - 1\right)^{3}}{1 - \left(x - 3 \log{\left(x^{2} + 1 \right)}\right)^{2}} + \frac{3 \left(x - 3 \log{\left(x^{2} + 1 \right)}\right)^{2} \left(\frac{6 x}{x^{2} + 1} - 1\right)^{3}}{\left(1 - \left(x - 3 \log{\left(x^{2} + 1 \right)}\right)^{2}\right)^{2}}}{\sqrt{1 - \left(x - 3 \log{\left(x^{2} + 1 \right)}\right)^{2}}}$$