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- Derivative of a implicit defined function
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How to use it?
- Derivative of:
- Derivative of 3
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Derivative of xex
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Derivative of ln(2x)
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Derivative of f(x)=xtanx
- Integral of d{x}:
- xex
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Identical expressions
- xex
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Similar expressions
- x*exp(-x)
- (asinx+bcosx)*exp(3x)
- x*exp(x)
- xe^(x)
- 2xe^x
Derivative of xex
The solution
You have entered
[src]
/ x\ \e / x
$$x^{e^{x}}$$
/ / x\\ d | \e /| --\x / dx
$$\frac{d}{d x} x^{e^{x}}$$
Detail solution
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Don't know the steps in finding this derivative.
But the derivative is
The answer is:
The first derivative
[src]
/ x\ / x \
\e / |e x |
x *|-- + e *log(x)|
\x /
$$x^{e^{x}} \left(e^{x} \log{\left(x \right)} + \frac{e^{x}}{x}\right)$$
The second derivative
[src]
/ x\ / 2 \
\e / | 1 2 /1 \ x | x
x *|- -- + - + |- + log(x)| *e + log(x)|*e
| 2 x \x / |
\ x /
$$x^{e^{x}} \left(\left(\log{\left(x \right)} + \frac{1}{x}\right)^{2} e^{x} + \log{\left(x \right)} + \frac{2}{x} - \frac{1}{x^{2}}\right) e^{x}$$
The third derivative
[src]
/ x\ / 3 \
\e / | 3 2 3 /1 \ 2*x /1 \ / 1 2 \ x | x
x *|- -- + -- + - + |- + log(x)| *e + 3*|- + log(x)|*|- -- + - + log(x)|*e + log(x)|*e
| 2 3 x \x / \x / | 2 x | |
\ x x \ x / /
$$x^{e^{x}} \left(\left(\log{\left(x \right)} + \frac{1}{x}\right)^{3} e^{2 x} + 3 \left(\log{\left(x \right)} + \frac{1}{x}\right) \left(\log{\left(x \right)} + \frac{2}{x} - \frac{1}{x^{2}}\right) e^{x} + \log{\left(x \right)} + \frac{3}{x} - \frac{3}{x^{2}} + \frac{2}{x^{3}}\right) e^{x}$$
The graph