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- Derivative of a implicit defined function
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- Partial derivative of the function
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- Differential equations Step by Step
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How to use it?
- Derivative of:
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Derivative of y=2x
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Derivative of x^2/e^x
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Derivative of (x-3)/(x+3)
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Derivative of x^3/(2*x+4)
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Identical expressions
- x^(2ln(x)/x(three))
- x to the power of (2ln(x) divide by x(3))
- x to the power of (2ln(x) divide by x(three))
- x(2ln(x)/x(3))
- x2lnx/x3
- x^2lnx/x3
- x^(2ln(x) divide by x(3))
Derivative of x^(2ln(x)/x(3))
The solution
You have entered
[src]
2*log(x)
--------*3
x
x
$$x^{3 \frac{2 \log{\left(x \right)}}{x}}$$
x^(((2*log(x))/x)*3)
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]
2*log(x)
--------*3
x //6 6*log(x)\ 6*log(x)\
x *||-- - --------|*log(x) + --------|
|| 2 2 | 2 |
\\x x / x /
$$x^{3 \frac{2 \log{\left(x \right)}}{x}} \left(\left(- \frac{6 \log{\left(x \right)}}{x^{2}} + \frac{6}{x^{2}}\right) \log{\left(x \right)} + \frac{6 \log{\left(x \right)}}{x^{2}}\right)$$
The second derivative
[src]
6*log(x)
-------- / 2 2 \
x | 6*(-2 + log(x)) *log (x)|
6*x *|2 - 3*log(x) + (-3 + 2*log(x))*log(x) + ------------------------|
\ x /
------------------------------------------------------------------------------
3
x
$$\frac{6 x^{\frac{6 \log{\left(x \right)}}{x}} \left(\left(2 \log{\left(x \right)} - 3\right) \log{\left(x \right)} - 3 \log{\left(x \right)} + 2 + \frac{6 \left(\log{\left(x \right)} - 2\right)^{2} \log{\left(x \right)}^{2}}{x}\right)}{x^{3}}$$
The third derivative
[src]
6*log(x)
-------- / 3 3 \
x | 36*(-2 + log(x)) *log (x) 18*(-2 + log(x))*(2 - 3*log(x) + (-3 + 2*log(x))*log(x))*log(x)|
6*x *|-12 + 11*log(x) - (-11 + 6*log(x))*log(x) - ------------------------- - ---------------------------------------------------------------|
| 2 x |
\ x /
-----------------------------------------------------------------------------------------------------------------------------------------------------
4
x
$$\frac{6 x^{\frac{6 \log{\left(x \right)}}{x}} \left(- \left(6 \log{\left(x \right)} - 11\right) \log{\left(x \right)} + 11 \log{\left(x \right)} - 12 - \frac{18 \left(\log{\left(x \right)} - 2\right) \left(\left(2 \log{\left(x \right)} - 3\right) \log{\left(x \right)} - 3 \log{\left(x \right)} + 2\right) \log{\left(x \right)}}{x} - \frac{36 \left(\log{\left(x \right)} - 2\right)^{3} \log{\left(x \right)}^{3}}{x^{2}}\right)}{x^{4}}$$