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How to use it?
- Derivative of:
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Derivative of x^(7/6)
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Derivative of x^4*e^x
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Derivative of e^x-7
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Derivative of (1-3x)^4
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Identical expressions
- arctg(two +(three /(x+ zero , one *x^ two)))
- arctg(2 plus (3 divide by (x plus 0,1 multiply by x squared )))
- arctg(two plus (three divide by (x plus zero , one multiply by x to the power of two)))
- arctg(2+(3/(x+0,1*x2)))
- arctg2+3/x+0,1*x2
- arctg(2+(3/(x+0,1*x²)))
- arctg(2+(3/(x+0,1*x to the power of 2)))
- arctg(2+(3/(x+0,1x^2)))
- arctg(2+(3/(x+0,1x2)))
- arctg2+3/x+0,1x2
- arctg2+3/x+0,1x^2
- arctg(2+(3 divide by (x+0,1*x^2)))
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Similar expressions
- arctg(2-(3/(x+0,1*x^2)))
- arctg(2+(3/(x-0,1*x^2)))
Derivative of arctg(2+(3/(x+0,1*x^2)))
The solution
You have entered
[src]
/ 3 \
atan|2 + ------|
| 2|
| x |
| x + --|
\ 10/
$$\operatorname{atan}{\left(2 + \frac{3}{\frac{x^{2}}{10} + x} \right)}$$
atan(2 + 3/(x + x^2/10))
The first derivative
[src]
/ x\
3*|-1 - -|
\ 5/
-----------------------------
2
/ 2\ / 2\
| / 3 \ | | x |
|1 + |2 + ------| |*|x + --|
| | 2| | \ 10/
| | x | |
| | x + --| |
\ \ 10/ /
$$\frac{3 \left(- \frac{x}{5} - 1\right)}{\left(\frac{x^{2}}{10} + x\right)^{2} \left(\left(2 + \frac{3}{\frac{x^{2}}{10} + x}\right)^{2} + 1\right)}$$
The second derivative
[src]
/ 2 / 15 \ \
| 2 240*(5 + x) *|1 + ----------| |
| 4*(5 + x) \ x*(10 + x)/ |
60*|-1 + ---------- - --------------------------------------|
| x*(10 + x) / 2\ |
| 2 | / 15 \ | 2|
| x *|1 + 4*|1 + ----------| |*(10 + x) |
\ \ \ x*(10 + x)/ / /
-------------------------------------------------------------
/ 2\
2 | / 15 \ | 2
x *|1 + 4*|1 + ----------| |*(10 + x)
\ \ x*(10 + x)/ /
$$\frac{60 \left(-1 + \frac{4 \left(x + 5\right)^{2}}{x \left(x + 10\right)} - \frac{240 \left(1 + \frac{15}{x \left(x + 10\right)}\right) \left(x + 5\right)^{2}}{x^{2} \left(x + 10\right)^{2} \left(4 \left(1 + \frac{15}{x \left(x + 10\right)}\right)^{2} + 1\right)}\right)}{x^{2} \left(x + 10\right)^{2} \left(4 \left(1 + \frac{15}{x \left(x + 10\right)}\right)^{2} + 1\right)}$$
The third derivative
[src]
/ 2 \
| / 15 \ / 15 \ 2 2 / 15 \ |
| 2 60*|1 + ----------| 2 9600*|1 + ----------| *(5 + x) 240*(5 + x) *|1 + ----------| |
| 2*(5 + x) \ x*(10 + x)/ 600*(5 + x) \ x*(10 + x)/ \ x*(10 + x)/ |
720*(5 + x)*|1 - ---------- - ------------------------------------ + -------------------------------------- - --------------------------------------- + --------------------------------------|
| x*(10 + x) / 2\ / 2\ 2 / 2\ |
| | / 15 \ | 3 | / 15 \ | 3 / 2\ 2 | / 15 \ | 2|
| x*|1 + 4*|1 + ----------| |*(10 + x) x *|1 + 4*|1 + ----------| |*(10 + x) 3 | / 15 \ | 3 x *|1 + 4*|1 + ----------| |*(10 + x) |
| \ \ x*(10 + x)/ / \ \ x*(10 + x)/ / x *|1 + 4*|1 + ----------| | *(10 + x) \ \ x*(10 + x)/ / |
\ \ \ x*(10 + x)/ / /
-----------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------
/ 2\
3 | / 15 \ | 3
x *|1 + 4*|1 + ----------| |*(10 + x)
\ \ x*(10 + x)/ /
$$\frac{720 \left(x + 5\right) \left(1 - \frac{60 \left(1 + \frac{15}{x \left(x + 10\right)}\right)}{x \left(x + 10\right) \left(4 \left(1 + \frac{15}{x \left(x + 10\right)}\right)^{2} + 1\right)} - \frac{2 \left(x + 5\right)^{2}}{x \left(x + 10\right)} + \frac{240 \left(1 + \frac{15}{x \left(x + 10\right)}\right) \left(x + 5\right)^{2}}{x^{2} \left(x + 10\right)^{2} \left(4 \left(1 + \frac{15}{x \left(x + 10\right)}\right)^{2} + 1\right)} - \frac{9600 \left(1 + \frac{15}{x \left(x + 10\right)}\right)^{2} \left(x + 5\right)^{2}}{x^{3} \left(x + 10\right)^{3} \left(4 \left(1 + \frac{15}{x \left(x + 10\right)}\right)^{2} + 1\right)^{2}} + \frac{600 \left(x + 5\right)^{2}}{x^{3} \left(x + 10\right)^{3} \left(4 \left(1 + \frac{15}{x \left(x + 10\right)}\right)^{2} + 1\right)}\right)}{x^{3} \left(x + 10\right)^{3} \left(4 \left(1 + \frac{15}{x \left(x + 10\right)}\right)^{2} + 1\right)}$$