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^2*e^2
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Derivative of x^3+2*x^5
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Derivative of e^(x*(-4))
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Derivative of (3*x-5)^6
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Identical expressions
- y=x^sqrt(lnx)
- y equally x to the power of square root of (lnx)
- y=x^√(lnx)
- y=xsqrt(lnx)
- y=xsqrtlnx
- y=x^sqrtlnx
Derivative of y=x^sqrt(lnx)
The solution
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]
________
\/ log(x) ________
3*x *\/ log(x)
------------------------
2*x
$$\frac{3 x^{\sqrt{\log{\left(x \right)}}} \sqrt{\log{\left(x \right)}}}{2 x}$$
The second derivative
[src]
________
\/ log(x) / 1 ________ \
3*x *|---------- - 2*\/ log(x) + 3*log(x)|
| ________ |
\\/ log(x) /
----------------------------------------------------
2
4*x
$$\frac{3 x^{\sqrt{\log{\left(x \right)}}} \left(- 2 \sqrt{\log{\left(x \right)}} + 3 \log{\left(x \right)} + \frac{1}{\sqrt{\log{\left(x \right)}}}\right)}{4 x^{2}}$$
The third derivative
[src]
________ / 3/2 \
\/ log(x) |9 ________ 9*log(x) 3 1 9*log (x)|
3*x *|- + \/ log(x) - -------- - ------------ - ----------- + -----------|
|8 4 ________ 3/2 8 |
\ 4*\/ log(x) 8*log (x) /
------------------------------------------------------------------------------------
3
x
$$\frac{3 x^{\sqrt{\log{\left(x \right)}}} \left(\frac{9 \log{\left(x \right)}^{\frac{3}{2}}}{8} + \sqrt{\log{\left(x \right)}} - \frac{9 \log{\left(x \right)}}{4} + \frac{9}{8} - \frac{3}{4 \sqrt{\log{\left(x \right)}}} - \frac{1}{8 \log{\left(x \right)}^{\frac{3}{2}}}\right)}{x^{3}}$$
The graph