Mister Exam
Other calculators
- 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 2e^x
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Derivative of x/(x+1)
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Derivative of x^(x^2)
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Derivative of x/log(x)
- Graphing y =:
- x^(x^2)
- Limit of the function:
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x^(x^2)
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Identical expressions
- x^(x^ two)
- x to the power of (x squared )
- x to the power of (x to the power of two)
- x(x2)
- xx2
- x^(x²)
- x to the power of (x to the power of 2)
- x^x^2
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Similar expressions
- x^2(ln(x+sinx))(x+sinx)^x^2
- x^(x^2+3x)
- y=(sinhx)^(x^2)
- y=(sqrt(5-x))^x^2
Derivative of x^(x^2)
The solution
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]
/ 2\ \x / x *(x + 2*x*log(x))
$$x^{x^{2}} \left(2 x \log{\left(x \right)} + x\right)$$
The second derivative
[src]
/ 2\ \x / / 2 2\ x *\3 + 2*log(x) + x *(1 + 2*log(x)) /
$$x^{x^{2}} \left(x^{2} \left(2 \log{\left(x \right)} + 1\right)^{2} + 2 \log{\left(x \right)} + 3\right)$$
The third derivative
[src]
/ 2\
\x / /2 3 3 \
x *|- + x *(1 + 2*log(x)) + 3*x*(1 + 2*log(x))*(3 + 2*log(x))|
\x /
$$x^{x^{2}} \left(x^{3} \left(2 \log{\left(x \right)} + 1\right)^{3} + 3 x \left(2 \log{\left(x \right)} + 1\right) \left(2 \log{\left(x \right)} + 3\right) + \frac{2}{x}\right)$$
The graph