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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-4)^2
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Derivative of x^2+4
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Derivative of x^2+4*x+3
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Derivative of sec
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Identical expressions
- three ^arctgx^ three
- 3 to the power of arctgx cubed
- three to the power of arctgx to the power of three
- 3arctgx3
- 3^arctgx³
- 3 to the power of arctgx to the power of 3
Derivative of 3^arctgx^3
The solution
The first derivative
[src]
3
acot (x) 2
-3*3 *acot (x)*log(3)
----------------------------
2
1 + x
$$- \frac{3 \cdot 3^{\operatorname{acot}^{3}{\left(x \right)}} \log{\left(3 \right)} \operatorname{acot}^{2}{\left(x \right)}}{x^{2} + 1}$$
The second derivative
[src]
3
acot (x) / 3 \
3*3 *\2 + 2*x*acot(x) + 3*acot (x)*log(3)/*acot(x)*log(3)
----------------------------------------------------------------
2
/ 2\
\1 + x /
$$\frac{3 \cdot 3^{\operatorname{acot}^{3}{\left(x \right)}} \left(2 x \operatorname{acot}{\left(x \right)} + 3 \log{\left(3 \right)} \operatorname{acot}^{3}{\left(x \right)} + 2\right) \log{\left(3 \right)} \operatorname{acot}{\left(x \right)}}{\left(x^{2} + 1\right)^{2}}$$
The third derivative
[src]
3 / 3 6 2 2 2 4 \
acot (x) | 2 2 18*acot (x)*log(3) 12*x*acot(x) 9*acot (x)*log (3) 8*x *acot (x) 18*x*acot (x)*log(3)|
3*3 *|- ------ + 2*acot (x) - ------------------ - ------------ - ------------------ - ------------- - --------------------|*log(3)
| 2 2 2 2 2 2 |
\ 1 + x 1 + x 1 + x 1 + x 1 + x 1 + x /
------------------------------------------------------------------------------------------------------------------------------------------
2
/ 2\
\1 + x /
$$\frac{3 \cdot 3^{\operatorname{acot}^{3}{\left(x \right)}} \left(- \frac{8 x^{2} \operatorname{acot}^{2}{\left(x \right)}}{x^{2} + 1} - \frac{18 x \log{\left(3 \right)} \operatorname{acot}^{4}{\left(x \right)}}{x^{2} + 1} - \frac{12 x \operatorname{acot}{\left(x \right)}}{x^{2} + 1} + 2 \operatorname{acot}^{2}{\left(x \right)} - \frac{9 \log{\left(3 \right)}^{2} \operatorname{acot}^{6}{\left(x \right)}}{x^{2} + 1} - \frac{18 \log{\left(3 \right)} \operatorname{acot}^{3}{\left(x \right)}}{x^{2} + 1} - \frac{2}{x^{2} + 1}\right) \log{\left(3 \right)}}{\left(x^{2} + 1\right)^{2}}$$
The graph