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^5*sin(x)
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Derivative of (x^2-x)/2
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Derivative of (x^2-1)/((2*x))
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Derivative of x^(-1/3)
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Identical expressions
- ln^(x- two)x
- ln to the power of (x minus 2)x
- ln to the power of (x minus two)x
- ln(x-2)x
- lnx-2x
- ln^x-2x
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Similar expressions
- ln^(x+2)x
Derivative of ln^(x-2)x
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]
x - 2 / x - 2 \
log (x)*|-------- + log(log(x))|
\x*log(x) /
$$\left(\log{\left(\log{\left(x \right)} \right)} + \frac{x - 2}{x \log{\left(x \right)}}\right) \log{\left(x \right)}^{x - 2}$$
The second derivative
[src]
/ -2 + x -2 + x \
| 2 -2 + ------ + --------|
-2 + x |/ -2 + x \ x x*log(x)|
log (x)*||-------- + log(log(x))| - ----------------------|
\\x*log(x) / x*log(x) /
$$\left(\left(\log{\left(\log{\left(x \right)} \right)} + \frac{x - 2}{x \log{\left(x \right)}}\right)^{2} - \frac{-2 + \frac{x - 2}{x} + \frac{x - 2}{x \log{\left(x \right)}}}{x \log{\left(x \right)}}\right) \log{\left(x \right)}^{x - 2}$$
The third derivative
[src]
/ 3 2*(-2 + x) 2*(-2 + x) 3*(-2 + x) \
| -3 - ------ + ---------- + ---------- + ---------- / -2 + x \ / -2 + x -2 + x \|
| 3 log(x) x 2 x*log(x) 3*|-------- + log(log(x))|*|-2 + ------ + --------||
-2 + x |/ -2 + x \ x*log (x) \x*log(x) / \ x x*log(x)/|
log (x)*||-------- + log(log(x))| + -------------------------------------------------- - ---------------------------------------------------|
|\x*log(x) / 2 x*log(x) |
\ x *log(x) /
$$\left(\left(\log{\left(\log{\left(x \right)} \right)} + \frac{x - 2}{x \log{\left(x \right)}}\right)^{3} - \frac{3 \left(\log{\left(\log{\left(x \right)} \right)} + \frac{x - 2}{x \log{\left(x \right)}}\right) \left(-2 + \frac{x - 2}{x} + \frac{x - 2}{x \log{\left(x \right)}}\right)}{x \log{\left(x \right)}} + \frac{-3 - \frac{3}{\log{\left(x \right)}} + \frac{2 \left(x - 2\right)}{x} + \frac{3 \left(x - 2\right)}{x \log{\left(x \right)}} + \frac{2 \left(x - 2\right)}{x \log{\left(x \right)}^{2}}}{x^{2} \log{\left(x \right)}}\right) \log{\left(x \right)}^{x - 2}$$