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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^(7/6)
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Derivative of e^x-7
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Derivative of 5^-x
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Derivative of x*sin(3*x)
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Identical expressions
- е^arctg(x/ three)
- е to the power of arctg(x divide by 3)
- е to the power of arctg(x divide by three)
- еarctg(x/3)
- еarctgx/3
- е^arctgx/3
- е^arctg(x divide by 3)
Derivative of е^arctg(x/3)
The solution
You have entered
[src]
/x\
atan|-|
\3/
E
$$e^{\operatorname{atan}{\left(\frac{x}{3} \right)}}$$
E^atan(x/3)
The first derivative
[src]
/x\
atan|-|
\3/
e
----------
/ 2\
| x |
3*|1 + --|
\ 9 /
$$\frac{e^{\operatorname{atan}{\left(\frac{x}{3} \right)}}}{3 \left(\frac{x^{2}}{9} + 1\right)}$$
The second derivative
[src]
/x\
atan|-|
\3/
3*(3 - 2*x)*e
--------------------
2
/ 2\
\9 + x /
$$\frac{3 \left(3 - 2 x\right) e^{\operatorname{atan}{\left(\frac{x}{3} \right)}}}{\left(x^{2} + 9\right)^{2}}$$
The third derivative
[src]
/x\
/ 2 \ atan|-|
| 9 18*x 8*x | \3/
3*|-2 + ------ - ------ + ------|*e
| 2 2 2|
\ 9 + x 9 + x 9 + x /
------------------------------------------
2
/ 2\
\9 + x /
$$\frac{3 \left(\frac{8 x^{2}}{x^{2} + 9} - \frac{18 x}{x^{2} + 9} - 2 + \frac{9}{x^{2} + 9}\right) e^{\operatorname{atan}{\left(\frac{x}{3} \right)}}}{\left(x^{2} + 9\right)^{2}}$$
The graph