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y=lg(2x^2+1)
The derivative of the function/ y=lg(2x^2+1)

Derivative of y=lg(2x^2+1)

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

The graph:

from to

Piecewise:

The solution

You have entered [src] 
   /   2    \
log\2*x  + 1/
$$\log{\left(2 x^{2} + 1 \right)}$$ 
log(2*x^2 + 1)
Detail solution

  1. Let .

  2. The derivative of is .

  3. Then, apply the chain rule. Multiply by :

    1. Differentiate 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: goes to

        So, the result is:

      2. The derivative of the constant is zero.

      The result is:

    The result of the chain rule is:

  4. Now simplify:

The answer is:

The graph
Plot the graph f(x)
Plot the graph f'(x)
The first derivative [src] 
  4*x   
--------
   2    
2*x  + 1
$$\frac{4 x}{2 x^{2} + 1}$$
Simplify
The second derivative [src] 
  /         2  \
  |      4*x   |
4*|1 - --------|
  |           2|
  \    1 + 2*x /
----------------
           2    
    1 + 2*x
$$\frac{4 \left(- \frac{4 x^{2}}{2 x^{2} + 1} + 1\right)}{2 x^{2} + 1}$$
Simplify
The third derivative [src] 
     /          2  \
     |       8*x   |
16*x*|-3 + --------|
     |            2|
     \     1 + 2*x /
--------------------
              2     
    /       2\      
    \1 + 2*x /
$$\frac{16 x \left(\frac{8 x^{2}}{2 x^{2} + 1} - 3\right)}{\left(2 x^{2} + 1\right)^{2}}$$
Simplify
The graph
Derivative of y=lg(2x^2+1)
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