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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 x^2*e^2
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Derivative of x^3+2*x^5
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Derivative of e^(x*(-4))
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Derivative of 2*x/(x^2+4)
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Identical expressions
- arctg*(x+ one)/x
- arctg multiply by (x plus 1) divide by x
- arctg multiply by (x plus one) divide by x
- arctg(x+1)/x
- arctgx+1/x
- arctg*(x+1) divide by x
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Similar expressions
- arctg*(x-1)/x
- (arctgx+1)/x
- arctgx+1/x-1
Derivative of arctg*(x+1)/x
The solution
You have entered
[src]
atan(x + 1)
-----------
x
$$\frac{\operatorname{atan}{\left(x + 1 \right)}}{x}$$
atan(x + 1)/x
The first derivative
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1 atan(x + 1) ---------------- - ----------- / 2\ 2 x*\1 + (x + 1) / x
$$\frac{1}{x \left(\left(x + 1\right)^{2} + 1\right)} - \frac{\operatorname{atan}{\left(x + 1 \right)}}{x^{2}}$$
The second derivative
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/atan(1 + x) 1 1 + x \
2*|----------- - ---------------- - ---------------|
| 2 / 2\ 2|
| x x*\1 + (1 + x) / / 2\ |
\ \1 + (1 + x) / /
----------------------------------------------------
x
$$\frac{2 \left(- \frac{x + 1}{\left(\left(x + 1\right)^{2} + 1\right)^{2}} - \frac{1}{x \left(\left(x + 1\right)^{2} + 1\right)} + \frac{\operatorname{atan}{\left(x + 1 \right)}}{x^{2}}\right)}{x}$$
The third derivative
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/ 2 \
| 4*(1 + x) |
|-1 + ------------ |
| 2 |
| 1 + (1 + x) 3*atan(1 + x) 3 3*(1 + x) |
2*|----------------- - ------------- + ----------------- + -----------------|
| 2 3 2 / 2\ 2|
| / 2\ x x *\1 + (1 + x) / / 2\ |
\ \1 + (1 + x) / x*\1 + (1 + x) / /
-----------------------------------------------------------------------------
x
$$\frac{2 \left(\frac{\frac{4 \left(x + 1\right)^{2}}{\left(x + 1\right)^{2} + 1} - 1}{\left(\left(x + 1\right)^{2} + 1\right)^{2}} + \frac{3 \left(x + 1\right)}{x \left(\left(x + 1\right)^{2} + 1\right)^{2}} + \frac{3}{x^{2} \left(\left(x + 1\right)^{2} + 1\right)} - \frac{3 \operatorname{atan}{\left(x + 1 \right)}}{x^{3}}\right)}{x}$$