Derivative of y=ln*x²

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   2   
log (x)

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

log(x)^2

Detail solution

Let $u = \log{\left(x \right)}$ .
Apply the power rule: $u^{2}$ goes to $2 u$
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:

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

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

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

Simplify

The third derivative [src]

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

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

Simplify

The graph