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Derivative of:
Derivative of log(2)
Derivative of 1/(x-1)
Derivative of x*ctgx
Derivative of sin(lnx)
Identical expressions
y=4ln^ two (x)
y equally 4ln squared (x)
y equally 4ln to the power of two (x)
y=4ln2(x)
y=4ln2x
y=4ln²(x)
y=4ln to the power of 2(x)
y=4ln^2x
Similar expressions
sin5^x/4*ln^2(x)

The derivative of the function/ y=4ln^2(x)

Derivative of y=4ln^2(x)

The solution

You have entered [src]

     2   
4*log (x)

$$4 \log{\left(x \right)}^{2}$$

d /     2   \
--\4*log (x)/
dx

$$\frac{d}{d x} 4 \log{\left(x \right)}^{2}$$

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: $\frac{8 \log{\left(x \right)}}{x}$

The answer is:

$\frac{8 \log{\left(x \right)}}{x}$

The graph

Plot the graph f(x)

Plot the graph f'(x)

The first derivative [src]

8*log(x)
--------
   x

$$\frac{8 \log{\left(x \right)}}{x}$$

Simplify

The second derivative [src]

-8*(-1 + log(x))
----------------
        2       
       x

$$- \frac{8 \left(\log{\left(x \right)} - 1\right)}{x^{2}}$$

Simplify

The third derivative [src]

8*(-3 + 2*log(x))
-----------------
         3       
        x

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

Simplify

The graph

Derivative of y=4ln^2(x)