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Derivative of:
Derivative of x^(1/x)
Derivative of 1/x^3
Derivative of cos(2*x)
Derivative of sin(x)^cos(x)
Identical expressions
(two *sqrt(x))*(ln(x)- two)
(2 multiply by square root of (x)) multiply by (ln(x) minus 2)
(two multiply by square root of (x)) multiply by (ln(x) minus two)
(2*√(x))*(ln(x)-2)
(2sqrt(x))(ln(x)-2)
2sqrtxlnx-2
Similar expressions
(2*sqrt(x))*(ln(x)+2)

The derivative of the function/ (2*sqrt(x))*(ln(x)-2)

Derivative of (2sqrt(x))(ln(x)-2)

The solution

You have entered [src]

    ___             
2*\/ x *(log(x) - 2)

$$2 \sqrt{x} \left(\log{\left(x \right)} - 2\right)$$

(2*sqrt(x))*(log(x) - 2)

Detail solution

Apply the product rule:

$\frac{d}{d x} f{\left(x \right)} g{\left(x \right)} = f{\left(x \right)} \frac{d}{d x} g{\left(x \right)} + g{\left(x \right)} \frac{d}{d x} f{\left(x \right)}$

$f{\left(x \right)} = 2 \sqrt{x}$ ; to find $\frac{d}{d x} f{\left(x \right)}$ :
1. The derivative of a constant times a function is the constant times the derivative of the function.
  1. Apply the power rule: $\sqrt{x}$ goes to $\frac{1}{2 \sqrt{x}}$
  So, the result is: $\frac{1}{\sqrt{x}}$
$g{\left(x \right)} = \log{\left(x \right)} - 2$ ; to find $\frac{d}{d x} g{\left(x \right)}$ :
1. Differentiate $\log{\left(x \right)} - 2$ term by term:
  1. The derivative of $\log{\left(x \right)}$ is $\frac{1}{x}$ .
  2. The derivative of the constant $-2$ is zero.
  The result is: $\frac{1}{x}$
The result is: $\frac{\log{\left(x \right)} - 2}{\sqrt{x}} + \frac{2}{\sqrt{x}}$
Now simplify:

$\frac{\log{\left(x \right)}}{\sqrt{x}}$

The answer is:

$\frac{\log{\left(x \right)}}{\sqrt{x}}$

The graph

Plot the graph f(x)

Plot the graph f'(x)

The first derivative [src]

  2     log(x) - 2
----- + ----------
  ___       ___   
\/ x      \/ x

$$\frac{\log{\left(x \right)} - 2}{\sqrt{x}} + \frac{2}{\sqrt{x}}$$

Simplify

The second derivative [src]

-(-2 + log(x)) 
---------------
        3/2    
     2*x

$$- \frac{\log{\left(x \right)} - 2}{2 x^{\frac{3}{2}}}$$

Simplify

The third derivative [src]

-8 + 3*log(x)
-------------
       5/2   
    4*x

$$\frac{3 \log{\left(x \right)} - 8}{4 x^{\frac{5}{2}}}$$

Simplify