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Derivative of:
Derivative of y=5x-6
Derivative of x^6*e^x
Derivative of x^5/5
Derivative of x^5-5*x^3-20*x
Identical expressions
-(ln(x))^ two
minus (ln(x)) squared
minus (ln(x)) to the power of two
-(ln(x))2
-lnx2
-(ln(x))²
-(ln(x)) to the power of 2
-lnx^2
Similar expressions
(ln(x))^2

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

Derivative of -(ln(x))^2

The solution

You have entered [src]

    2   
-log (x)

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

d /    2   \
--\-log (x)/
dx

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

Transform

Detail solution

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 answer is:

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

The graph

Plot the graph f(x)

Plot the graph f'(x)

The first derivative [src]

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

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

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

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

Simplify

The graph

Derivative of -(ln(x))^2