Mister Exam

Lang:

Other calculators

How to use it?
Derivative of:
Derivative of x^x^x
Derivative of x^-11
Derivative of (x+5)/(x+1)
Derivative of x^(4/3)
Graphing y =:
x-(ln(x))^2
Identical expressions
x-(ln(x))^ two
x minus (ln(x)) squared
x minus (ln(x)) to the power of two
x-(ln(x))2
x-lnx2
x-(ln(x))²
x-(ln(x)) to the power of 2
x-lnx^2
Similar expressions
x+(ln(x))^2

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

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

The solution

You have entered [src]

       2   
x - log (x)

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

x - log(x)^2

Detail solution

Differentiate $x - \log{\left(x \right)}^{2}$ term by term:
1. Apply the power rule: $x$ goes to $1$
2. The derivative of a constant times a function is the constant times the derivative of the function.
  1. Let $u = \log{\left(x \right)}$ .
  2. Apply the power rule: $u^{2}$ goes to $2 u$
  3. Then, apply the chain rule. Multiply by $\frac{d}{d x} \log{\left(x \right)}$ :
    1. The derivative of $\log{\left(x \right)}$ is $\frac{1}{x}$ .
    The result of the chain rule is:
    
    $\frac{2 \log{\left(x \right)}}{x}$
  So, the result is: $- \frac{2 \log{\left(x \right)}}{x}$
The result is: $1 - \frac{2 \log{\left(x \right)}}{x}$
Now simplify:

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

The answer is:

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

The graph

Plot the graph f(x)

Plot the graph f'(x)

The first derivative [src]

    2*log(x)
1 - --------
       x

$$1 - \frac{2 \log{\left(x \right)}}{x}$$

Simplify

The second derivative [src]

2*(-1 + log(x))
---------------
        2      
       x

$$\frac{2 \left(\log{\left(x \right)} - 1\right)}{x^{2}}$$

Simplify

The third derivative [src]

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

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

Simplify

The graph

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