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The derivative of the function/ sqrtx-2lnx

Derivative of sqrtx-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)
$$\sqrt{x} - 2 \log{\left(x \right)}$$ 
sqrt(x) - 2*log(x)
Detail solution

  1. Differentiate term by term:

    1. Apply the power rule: goes to

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

      1. The derivative of is .

      So, the result is:

    The result is:

The answer is:

The graph
Plot the graph f(x)
Plot the graph f'(x)
The first derivative [src] 
   1      2
------- - -
    ___   x
2*\/ x
$$- \frac{2}{x} + \frac{1}{2 \sqrt{x}}$$
Simplify
The second derivative [src] 
2      1   
-- - ------
 2      3/2
x    4*x
$$\frac{2}{x^{2}} - \frac{1}{4 x^{\frac{3}{2}}}$$
Simplify
The third derivative [src] 
  4      3   
- -- + ------
   3      5/2
  x    8*x
$$- \frac{4}{x^{3}} + \frac{3}{8 x^{\frac{5}{2}}}$$
Simplify
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