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

Derivative of y=4ln^2(x)

Function f() - derivative -N order at the point
v

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The solution

You have entered [src] 
     2   
4*log (x)
4log⁡(x)24 \log{\left(x \right)}^{2} 
d /     2   \
--\4*log (x)/
dx
ddx4log⁡(x)2\frac{d}{d x} 4 \log{\left(x \right)}^{2}
Transform
Detail solution

  1. The derivative of a constant times a function is the constant times the derivative of the function.

    1. Let u=log⁡(x)u = \log{\left(x \right)}.

    2. Apply the power rule: u2u^{2} goes to 2u2 u

    3. Then, apply the chain rule. Multiply by ddxlog⁡(x)\frac{d}{d x} \log{\left(x \right)}:

      1. The derivative of log⁡(x)\log{\left(x \right)} is 1x\frac{1}{x}.

      The result of the chain rule is:

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

    So, the result is: 8log⁡(x)x\frac{8 \log{\left(x \right)}}{x}

The answer is:

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

The graph
02468-8-6-4-2-1010-200200
Plot the graph f(x)
Plot the graph f'(x)
The first derivative [src] 
8*log(x)
--------
   x
8log⁡(x)x\frac{8 \log{\left(x \right)}}{x}
Simplify
The second derivative [src] 
-8*(-1 + log(x))
----------------
        2       
       x
−8(log⁡(x)−1)x2- \frac{8 \left(\log{\left(x \right)} - 1\right)}{x^{2}}
Simplify
The third derivative [src] 
8*(-3 + 2*log(x))
-----------------
         3       
        x
8⋅(2log⁡(x)−3)x3\frac{8 \cdot \left(2 \log{\left(x \right)} - 3\right)}{x^{3}}
Simplify
The graph
Derivative of y=4ln^2(x)
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