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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 (-2)/x^3
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Derivative of ln(x^2-4x)
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Derivative of e^(3/x)
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Derivative of (2*x+1)*(x^2+3*x-1)
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Identical expressions
- y=exp^(-x)*arctg(x/ three)
- y equally exponent of to the power of ( minus x) multiply by arctg(x divide by 3)
- y equally exponent of to the power of ( minus x) multiply by arctg(x divide by three)
- y=exp(-x)*arctg(x/3)
- y=exp-x*arctgx/3
- y=exp^(-x)arctg(x/3)
- y=exp(-x)arctg(x/3)
- y=exp-xarctgx/3
- y=exp^-xarctgx/3
- y=exp^(-x)*arctg(x divide by 3)
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Similar expressions
- y=exp^(x)*arctg(x/3)
Derivative of y=exp^(-x)*arctg(x/3)
The solution
You have entered
[src]
-x /x\
E *atan|-|
\3/
$$e^{- x} \operatorname{atan}{\left(\frac{x}{3} \right)}$$
E^(-x)*atan(x/3)
The first derivative
[src]
-x
/x\ -x e
- atan|-|*e + ----------
\3/ / 2\
| x |
3*|1 + --|
\ 9 /
$$- e^{- x} \operatorname{atan}{\left(\frac{x}{3} \right)} + \frac{e^{- x}}{3 \left(\frac{x^{2}}{9} + 1\right)}$$
The second derivative
[src]
/ 6 6*x /x\\ -x |- ------ - --------- + atan|-||*e | 2 2 \3/| | 9 + x / 2\ | \ \9 + x / /
$$\left(- \frac{6 x}{\left(x^{2} + 9\right)^{2}} + \operatorname{atan}{\left(\frac{x}{3} \right)} - \frac{6}{x^{2} + 9}\right) e^{- x}$$
The third derivative
[src]
/ / 2 \ \ | | 4*x | | | 6*|-1 + ------| | | | 2| | | /x\ 9 \ 9 + x / 18*x | -x |- atan|-| + ------ + --------------- + ---------|*e | \3/ 2 2 2| | 9 + x / 2\ / 2\ | \ \9 + x / \9 + x / /
$$\left(\frac{18 x}{\left(x^{2} + 9\right)^{2}} - \operatorname{atan}{\left(\frac{x}{3} \right)} + \frac{9}{x^{2} + 9} + \frac{6 \left(\frac{4 x^{2}}{x^{2} + 9} - 1\right)}{\left(x^{2} + 9\right)^{2}}\right) e^{- x}$$
The graph