Mister Exam
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- Derivative of a implicit defined function
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- Partial derivative of the function
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How to use it?
- Derivative of:
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Derivative of cos(x/3)
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Derivative of √x
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Derivative of xcos(x)
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Derivative of ln1
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Identical expressions
- actg^(five)*(ln9x)
- actg to the power of (5) multiply by (ln9x)
- actg to the power of (five) multiply by (ln9x)
- actg(5)*(ln9x)
- actg5*ln9x
- actg^(5)(ln9x)
- actg(5)(ln9x)
- actg5ln9x
- actg^5ln9x
Derivative of actg^(5)*(ln9x)
The solution
You have entered
[src]
5 atan (log(9*x))
$$\operatorname{atan}^{5}{\left(\log{\left(9 x \right)} \right)}$$
atan(log(9*x))^5
The first derivative
[src]
4 5*atan (log(9*x)) ----------------- / 2 \ x*\1 + log (9*x)/
$$\frac{5 \operatorname{atan}^{4}{\left(\log{\left(9 x \right)} \right)}}{x \left(\log{\left(9 x \right)}^{2} + 1\right)}$$
The second derivative
[src]
3 / 4 2*atan(log(9*x))*log(9*x)\
5*atan (log(9*x))*|-atan(log(9*x)) + ------------- - -------------------------|
| 2 2 |
\ 1 + log (9*x) 1 + log (9*x) /
-------------------------------------------------------------------------------
2 / 2 \
x *\1 + log (9*x)/
$$\frac{5 \left(- \operatorname{atan}{\left(\log{\left(9 x \right)} \right)} - \frac{2 \log{\left(9 x \right)} \operatorname{atan}{\left(\log{\left(9 x \right)} \right)}}{\log{\left(9 x \right)}^{2} + 1} + \frac{4}{\log{\left(9 x \right)}^{2} + 1}\right) \operatorname{atan}^{3}{\left(\log{\left(9 x \right)} \right)}}{x^{2} \left(\log{\left(9 x \right)}^{2} + 1\right)}$$
The third derivative
[src]
/ 2 2 2 2 \
2 | 2 6 atan (log(9*x)) 6*atan(log(9*x)) 12*atan(log(9*x))*log(9*x) 3*atan (log(9*x))*log(9*x) 4*atan (log(9*x))*log (9*x)|
10*atan (log(9*x))*|atan (log(9*x)) + ---------------- - --------------- - ---------------- - -------------------------- + -------------------------- + ---------------------------|
| 2 2 2 2 2 2 |
| / 2 \ 1 + log (9*x) 1 + log (9*x) / 2 \ 1 + log (9*x) / 2 \ |
\ \1 + log (9*x)/ \1 + log (9*x)/ \1 + log (9*x)/ /
------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------
3 / 2 \
x *\1 + log (9*x)/
$$\frac{10 \left(\operatorname{atan}^{2}{\left(\log{\left(9 x \right)} \right)} + \frac{3 \log{\left(9 x \right)} \operatorname{atan}^{2}{\left(\log{\left(9 x \right)} \right)}}{\log{\left(9 x \right)}^{2} + 1} - \frac{\operatorname{atan}^{2}{\left(\log{\left(9 x \right)} \right)}}{\log{\left(9 x \right)}^{2} + 1} - \frac{6 \operatorname{atan}{\left(\log{\left(9 x \right)} \right)}}{\log{\left(9 x \right)}^{2} + 1} + \frac{4 \log{\left(9 x \right)}^{2} \operatorname{atan}^{2}{\left(\log{\left(9 x \right)} \right)}}{\left(\log{\left(9 x \right)}^{2} + 1\right)^{2}} - \frac{12 \log{\left(9 x \right)} \operatorname{atan}{\left(\log{\left(9 x \right)} \right)}}{\left(\log{\left(9 x \right)}^{2} + 1\right)^{2}} + \frac{6}{\left(\log{\left(9 x \right)}^{2} + 1\right)^{2}}\right) \operatorname{atan}^{2}{\left(\log{\left(9 x \right)} \right)}}{x^{3} \left(\log{\left(9 x \right)}^{2} + 1\right)}$$