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lnx^2-1
The derivative of the function/ lnx^2-1

Derivative of lnx^2-1

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

The graph:

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The solution

You have entered [src] 
   2       
log (x) - 1
log⁡(x)2−1\log{\left(x \right)}^{2} - 1 
d /   2       \
--\log (x) - 1/
dx
ddx(log⁡(x)2−1)\frac{d}{d x} \left(\log{\left(x \right)}^{2} - 1\right)
Transform
Detail solution

  1. Differentiate log⁡(x)2−1\log{\left(x \right)}^{2} - 1 term by term:

    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}

    4. The derivative of the constant (−1)1\left(-1\right) 1 is zero.

    The result is: 2log⁡(x)x\frac{2 \log{\left(x \right)}}{x}

The answer is:

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

The graph
02468-8-6-4-2-1010-5050
Plot the graph f(x)
Plot the graph f'(x)
The first derivative [src] 
2*log(x)
--------
   x
2log⁡(x)x\frac{2 \log{\left(x \right)}}{x}
Simplify
The second derivative [src] 
2*(1 - log(x))
--------------
       2      
      x
2⋅(−log⁡(x)+1)x2\frac{2 \cdot \left(- \log{\left(x \right)} + 1\right)}{x^{2}}
Simplify
The third derivative [src] 
2*(-3 + 2*log(x))
-----------------
         3       
        x
2⋅(2log⁡(x)−3)x3\frac{2 \cdot \left(2 \log{\left(x \right)} - 3\right)}{x^{3}}
Simplify
The graph
Derivative of lnx^2-1
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