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+5
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Derivative of e^sinx
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Derivative of x^2/(x+1)
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Derivative of x^1/5
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Identical expressions
- x*(e^|x|− one)/|x|
- x multiply by (e to the power of module of x|−1) divide by |x|
- x multiply by (e to the power of module of x|− one) divide by |x|
- x*(e|x|−1)/|x|
- x*e|x|−1/|x|
- x(e^|x|−1)/|x|
- x(e|x|−1)/|x|
- xe|x|−1/|x|
- xe^|x|−1/|x|
- x*(e^|x|−1) divide by |x|
Derivative of x*(e^|x|−1)/|x|
The solution
You have entered
[src]
/ |x| \
x*\E - 1/
------------
|x|
$$\frac{x \left(e^{\left|{x}\right|} - 1\right)}{\left|{x}\right|}$$
(x*(E^|x| - 1))/|x|
The first derivative
[src]
|x| |x| / |x| \
-1 + E + x*e *sign(x) \E - 1/*sign(x)
-------------------------- - ------------------
|x| x
$$\frac{e^{\left|{x}\right|} + x e^{\left|{x}\right|} \operatorname{sign}{\left(x \right)} - 1}{\left|{x}\right|} - \frac{\left(e^{\left|{x}\right|} - 1\right) \operatorname{sign}{\left(x \right)}}{x}$$
The second derivative
[src]
/ |x|\ / sign(x) \
/ / 2 \\ |x| 2*\-1 + e /*|- ------- + DiracDelta(x)| / |x| |x|\
\2*sign(x) + x*\sign (x) + 2*DiracDelta(x)//*e \ x / 2*\-1 + x*e *sign(x) + e /*sign(x)
------------------------------------------------- - ----------------------------------------- - --------------------------------------
|x| x 2
x
$$\frac{\left(x \left(2 \delta\left(x\right) + \operatorname{sign}^{2}{\left(x \right)}\right) + 2 \operatorname{sign}{\left(x \right)}\right) e^{\left|{x}\right|}}{\left|{x}\right|} - \frac{2 \left(e^{\left|{x}\right|} - 1\right) \left(\delta\left(x\right) - \frac{\operatorname{sign}{\left(x \right)}}{x}\right)}{x} - \frac{2 \left(x e^{\left|{x}\right|} \operatorname{sign}{\left(x \right)} + e^{\left|{x}\right|} - 1\right) \operatorname{sign}{\left(x \right)}}{x^{2}}$$
The third derivative
[src]
/ |x|\ / 4*DiracDelta(x) 3*sign(x) \
/ sign(x) \ / |x| |x|\ 2*\-1 + e /*|- --------------- + --------- + DiracDelta(x, 1)|
/ 2 / 3 \\ |x| 6*|- ------- + DiracDelta(x)|*\-1 + x*e *sign(x) + e / | x 2 | / / 2 \\ |x|
\3*sign (x) + 6*DiracDelta(x) + x*\sign (x) + 2*DiracDelta(x, 1) + 6*DiracDelta(x)*sign(x)//*e \ x / \ x / 3*\2*sign(x) + x*\sign (x) + 2*DiracDelta(x)//*e *sign(x)
------------------------------------------------------------------------------------------------- - ---------------------------------------------------------- - ---------------------------------------------------------------- - -----------------------------------------------------------
|x| 2 x 2
x x
$$\frac{\left(x \left(6 \delta\left(x\right) \operatorname{sign}{\left(x \right)} + 2 \delta^{\left( 1 \right)}\left( x \right) + \operatorname{sign}^{3}{\left(x \right)}\right) + 6 \delta\left(x\right) + 3 \operatorname{sign}^{2}{\left(x \right)}\right) e^{\left|{x}\right|}}{\left|{x}\right|} - \frac{2 \left(e^{\left|{x}\right|} - 1\right) \left(\delta^{\left( 1 \right)}\left( x \right) - \frac{4 \delta\left(x\right)}{x} + \frac{3 \operatorname{sign}{\left(x \right)}}{x^{2}}\right)}{x} - \frac{3 \left(x \left(2 \delta\left(x\right) + \operatorname{sign}^{2}{\left(x \right)}\right) + 2 \operatorname{sign}{\left(x \right)}\right) e^{\left|{x}\right|} \operatorname{sign}{\left(x \right)}}{x^{2}} - \frac{6 \left(\delta\left(x\right) - \frac{\operatorname{sign}{\left(x \right)}}{x}\right) \left(x e^{\left|{x}\right|} \operatorname{sign}{\left(x \right)} + e^{\left|{x}\right|} - 1\right)}{x^{2}}$$