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x-2lnx
The derivative of the function/ x-2lnx

Derivative of x-2lnx

Function f() - derivative -N order at the point
v

The graph:

from to

Piecewise:

The solution

You have entered [src] 
x - 2*log(x)
x−2log⁡(x)x - 2 \log{\left(x \right)} 
x - 2*log(x)
Detail solution

  1. Differentiate x−2log⁡(x)x - 2 \log{\left(x \right)} term by term:

    1. Apply the power rule: xx goes to 11

    2. The derivative of a constant times a function is the constant times the derivative of the function.

      1. The derivative of log⁡(x)\log{\left(x \right)} is 1x\frac{1}{x}.

      So, the result is: −2x- \frac{2}{x}

    The result is: 1−2x1 - \frac{2}{x}

  2. Now simplify:

    x−2x\frac{x - 2}{x}

The answer is:

x−2x\frac{x - 2}{x}

The graph
02468-8-6-4-2-1010-5050
Plot the graph f(x)
Plot the graph f'(x)
The first derivative [src] 
    2
1 - -
    x
1−2x1 - \frac{2}{x}
Simplify
The second derivative [src] 
2 
--
 2
x
2x2\frac{2}{x^{2}}
Simplify
The third derivative [src] 
-4 
---
  3
 x
−4x3- \frac{4}{x^{3}}
Simplify
The graph
Derivative of x-2lnx
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