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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^12
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Derivative of e^-1
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Derivative of sin^3*x
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Derivative of sen2x
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Identical expressions
- atan(e^x- three)/ two
- arc tangent of gent of (e to the power of x minus 3) divide by 2
- arc tangent of gent of (e to the power of x minus three) divide by two
- atan(ex-3)/2
- atanex-3/2
- atane^x-3/2
- atan(e^x-3) divide by 2
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Similar expressions
- atan(e^x+3)/2
- arctan(e^x-3)/2
Derivative of atan(e^x-3)/2
The solution
You have entered
[src]
/ x \
atan\E - 3/
------------
2
$$\frac{\operatorname{atan}{\left(e^{x} - 3 \right)}}{2}$$
atan(E^x - 3)/2
The first derivative
[src]
x
e
-----------------
/ 2\
| / x \ |
2*\1 + \E - 3/ /
$$\frac{e^{x}}{2 \left(\left(e^{x} - 3\right)^{2} + 1\right)}$$
The second derivative
[src]
/ / x\ x\
| 2*\-3 + e /*e | x
|1 - --------------|*e
| 2|
| / x\ |
\ 1 + \-3 + e / /
-----------------------
/ 2\
| / x\ |
2*\1 + \-3 + e / /
$$\frac{\left(1 - \frac{2 \left(e^{x} - 3\right) e^{x}}{\left(e^{x} - 3\right)^{2} + 1}\right) e^{x}}{2 \left(\left(e^{x} - 3\right)^{2} + 1\right)}$$
The third derivative
[src]
/ 2 \
| 2*x / x\ x / x\ 2*x|
| 2*e 6*\-3 + e /*e 8*\-3 + e / *e | x
|1 - -------------- - -------------- + -----------------|*e
| 2 2 2|
| / x\ / x\ / 2\ |
| 1 + \-3 + e / 1 + \-3 + e / | / x\ | |
\ \1 + \-3 + e / / /
------------------------------------------------------------
/ 2\
| / x\ |
2*\1 + \-3 + e / /
$$\frac{\left(1 - \frac{6 \left(e^{x} - 3\right) e^{x}}{\left(e^{x} - 3\right)^{2} + 1} - \frac{2 e^{2 x}}{\left(e^{x} - 3\right)^{2} + 1} + \frac{8 \left(e^{x} - 3\right)^{2} e^{2 x}}{\left(\left(e^{x} - 3\right)^{2} + 1\right)^{2}}\right) e^{x}}{2 \left(\left(e^{x} - 3\right)^{2} + 1\right)}$$