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ln(2x^2+3)
The derivative of the function/ ln(2x^2+3)

Derivative of ln(2x^2+3)

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

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The solution

You have entered [src] 
   /   2    \
log\2*x  + 3/
log⁡(2x2+3)\log{\left(2 x^{2} + 3 \right)} 
d /   /   2    \\
--\log\2*x  + 3//
dx
ddxlog⁡(2x2+3)\frac{d}{d x} \log{\left(2 x^{2} + 3 \right)}
Transform
Detail solution

  1. Let u=2x2+3u = 2 x^{2} + 3.

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

  3. Then, apply the chain rule. Multiply by ddx(2x2+3)\frac{d}{d x} \left(2 x^{2} + 3\right):

    1. Differentiate 2x2+32 x^{2} + 3 term by term:

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

        1. Apply the power rule: x2x^{2} goes to 2x2 x

        So, the result is: 4x4 x

      2. The derivative of the constant 33 is zero.

      The result is: 4x4 x

    The result of the chain rule is:

    4x2x2+3\frac{4 x}{2 x^{2} + 3}

  4. Now simplify:

    4x2x2+3\frac{4 x}{2 x^{2} + 3}

The answer is:

4x2x2+3\frac{4 x}{2 x^{2} + 3}

The graph
02468-8-6-4-2-1010-510
Plot the graph f(x)
Plot the graph f'(x)
The first derivative [src] 
  4*x   
--------
   2    
2*x  + 3
4x2x2+3\frac{4 x}{2 x^{2} + 3}
Simplify
The second derivative [src] 
  /         2  \
  |      4*x   |
4*|1 - --------|
  |           2|
  \    3 + 2*x /
----------------
           2    
    3 + 2*x
4(−4x22x2+3+1)2x2+3\frac{4 \left(- \frac{4 x^{2}}{2 x^{2} + 3} + 1\right)}{2 x^{2} + 3}
Simplify
The third derivative [src] 
     /          2  \
     |       8*x   |
16*x*|-3 + --------|
     |            2|
     \     3 + 2*x /
--------------------
              2     
    /       2\      
    \3 + 2*x /
16x(8x22x2+3−3)(2x2+3)2\frac{16 x \left(\frac{8 x^{2}}{2 x^{2} + 3} - 3\right)}{\left(2 x^{2} + 3\right)^{2}}
Simplify
The graph
Derivative of ln(2x^2+3)
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