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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 7x
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Derivative of e^(2*cos(t)^(2)-2*sin(t)^(2))
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Derivative of 4/x^3
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Derivative of 4*sqrt(x)
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Identical expressions
- one / two arctg((e^x- three)/2)
- 1 divide by 2arctg((e to the power of x minus 3) divide by 2)
- one divide by two arctg((e to the power of x minus three) divide by 2)
- 1/2arctg((ex-3)/2)
- 1/2arctgex-3/2
- 1/2arctge^x-3/2
- 1 divide by 2arctg((e^x-3) divide by 2)
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Similar expressions
- 1/2arctg((e^x+3)/2)
- (1/2)*arctg((e^x-3)/2)
Derivative of 1/2arctg((e^x-3)/2)
The solution
You have entered
[src]
/ x \
|e - 3|
atan|------|
\ 2 /
------------
2
$$\frac{\operatorname{atan}{\left(\frac{e^{x} - 3}{2} \right)}}{2}$$
/ / x \\ | |e - 3|| |atan|------|| d | \ 2 /| --|------------| dx\ 2 /
$$\frac{d}{d x} \frac{\operatorname{atan}{\left(\frac{e^{x} - 3}{2} \right)}}{2}$$
The first derivative
[src]
x
e
-----------------
/ 2\
| / x \ |
| \e - 3/ |
4*|1 + ---------|
\ 4 /
$$\frac{e^{x}}{4 \left(\frac{\left(e^{x} - 3\right)^{2}}{4} + 1\right)}$$
The second derivative
[src]
/ / x\ x\
| 2*\-3 + e /*e | x
|1 - --------------|*e
| 2|
| / x\ |
\ 4 + \-3 + e / /
-----------------------
2
/ x\
4 + \-3 + e /
$$\frac{\left(1 - \frac{2 \left(e^{x} - 3\right) e^{x}}{\left(e^{x} - 3\right)^{2} + 4}\right) e^{x}}{\left(e^{x} - 3\right)^{2} + 4}$$
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\ |
| 4 + \-3 + e / 4 + \-3 + e / | / x\ | |
\ \4 + \-3 + e / / /
------------------------------------------------------------
2
/ x\
4 + \-3 + e /
$$\frac{\left(1 - \frac{6 \left(e^{x} - 3\right) e^{x}}{\left(e^{x} - 3\right)^{2} + 4} - \frac{2 e^{2 x}}{\left(e^{x} - 3\right)^{2} + 4} + \frac{8 \left(e^{x} - 3\right)^{2} e^{2 x}}{\left(\left(e^{x} - 3\right)^{2} + 4\right)^{2}}\right) e^{x}}{\left(e^{x} - 3\right)^{2} + 4}$$
The graph