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 x^2-7*x
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Derivative of ln(1-x)
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Derivative of ln(-x)
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Derivative of ln(x+2)
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Identical expressions
- atan(y+ two -y^ two)
- arc tangent of gent of (y plus 2 minus y squared )
- arc tangent of gent of (y plus two minus y to the power of two)
- atan(y+2-y2)
- atany+2-y2
- atan(y+2-y²)
- atan(y+2-y to the power of 2)
- atany+2-y^2
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Similar expressions
- atan(y+2+y^2)
- atan(y-2-y^2)
- arctan(y+2-y^2)
Derivative of atan(y+2-y^2)
The solution
You have entered
[src]
/ 2\ atan\y + 2 - y /
$$\operatorname{atan}{\left(- y^{2} + \left(y + 2\right) \right)}$$
atan(y + 2 - y^2)
The first derivative
[src]
1 - 2*y
-----------------
2
/ 2\
1 + \y + 2 - y /
$$\frac{1 - 2 y}{\left(- y^{2} + \left(y + 2\right)\right)^{2} + 1}$$
The second derivative
[src]
/ 2 / 2\\
| (-1 + 2*y) *\2 + y - y /|
-2*|1 + ------------------------|
| 2 |
| / 2\ |
\ 1 + \2 + y - y / /
---------------------------------
2
/ 2\
1 + \2 + y - y /
$$- \frac{2 \left(\frac{\left(2 y - 1\right)^{2} \left(- y^{2} + y + 2\right)}{\left(- y^{2} + y + 2\right)^{2} + 1} + 1\right)}{\left(- y^{2} + y + 2\right)^{2} + 1}$$
The third derivative
[src]
/ 2\
| 2 / 2\ |
| 2 2 4*(-1 + 2*y) *\2 + y - y / |
2*(-1 + 2*y)*|-12 + (-1 + 2*y) - 6*y + 6*y - ---------------------------|
| 2 |
| / 2\ |
\ 1 + \2 + y - y / /
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2
/ 2\
| / 2\ |
\1 + \2 + y - y / /
$$\frac{2 \left(2 y - 1\right) \left(6 y^{2} - 6 y + \left(2 y - 1\right)^{2} - \frac{4 \left(2 y - 1\right)^{2} \left(- y^{2} + y + 2\right)^{2}}{\left(- y^{2} + y + 2\right)^{2} + 1} - 12\right)}{\left(\left(- y^{2} + y + 2\right)^{2} + 1\right)^{2}}$$