Mister Exam
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- Derivative of a implicit defined function
- Derivative of Parametric Function
- Partial derivative of the function
- Curve tracing functions Step by Step
- Integral Step by Step
- Differential equations Step by Step
- Limits Step by Step
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How to use it?
- Derivative of:
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Derivative of x^(1/x)
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Derivative of sin^2(2x)
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Derivative of 2x^2
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Derivative of sin(y)
- Integral of d{x}:
- x^(1/x)
- Graphing y =:
- x^(1/x)
- Limit of the function:
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x^(1/x)
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Identical expressions
- x^(one /x)
- x to the power of (1 divide by x)
- x to the power of (one divide by x)
- x(1/x)
- x1/x
- x^1/x
- x^(1 divide by x)
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Similar expressions
- (arcsinx/x)^(1/x^2)
- (1/x)^(1/x)
Derivative of x^(1/x)
The solution
You have entered
[src]
x ___ \/ x
$$x^{1 \cdot \frac{1}{x}}$$
d /x ___\ --\\/ x / dx
$$\frac{d}{d x} x^{1 \cdot \frac{1}{x}}$$
Detail solution
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Don't know the steps in finding this derivative.
But the derivative is
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Now simplify:
The answer is:
The first derivative
[src]
x ___ /1 log(x)\
\/ x *|-- - ------|
| 2 2 |
\x x /
$$x^{\frac{1}{x}} \left(- \frac{\log{\left(x \right)}}{x^{2}} + \frac{1}{x^{2}}\right)$$
The second derivative
[src]
/ 2\
x ___ | (-1 + log(x)) |
\/ x *|-3 + 2*log(x) + --------------|
\ x /
--------------------------------------
3
x
$$\frac{x^{\frac{1}{x}} \left(2 \log{\left(x \right)} - 3 + \frac{\left(\log{\left(x \right)} - 1\right)^{2}}{x}\right)}{x^{3}}$$
The third derivative
[src]
/ 3 \
x ___ | (-1 + log(x)) 3*(-1 + log(x))*(-3 + 2*log(x))|
-\/ x *|-11 + 6*log(x) + -------------- + -------------------------------|
| 2 x |
\ x /
---------------------------------------------------------------------------
4
x
$$- \frac{x^{\frac{1}{x}} \left(6 \log{\left(x \right)} - 11 + \frac{3 \left(\log{\left(x \right)} - 1\right) \left(2 \log{\left(x \right)} - 3\right)}{x} + \frac{\left(\log{\left(x \right)} - 1\right)^{3}}{x^{2}}\right)}{x^{4}}$$
The graph