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y=ln(9x^2+2)
The derivative of the function/ y=ln(9x^2+2)

Derivative of y=ln(9x^2+2)

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

The graph:

from to

Piecewise:

The solution

You have entered [src] 
   /   2    \
log\9*x  + 2/
$$\log{\left(9 x^{2} + 2 \right)}$$ 
log(9*x^2 + 2)
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] 
  18*x  
--------
   2    
9*x  + 2
$$\frac{18 x}{9 x^{2} + 2}$$
Simplify
The second derivative [src] 
   /         2  \
   |     18*x   |
18*|1 - --------|
   |           2|
   \    2 + 9*x /
-----------------
            2    
     2 + 9*x
$$\frac{18 \left(- \frac{18 x^{2}}{9 x^{2} + 2} + 1\right)}{9 x^{2} + 2}$$
Simplify
The third derivative [src] 
      /          2  \
      |      12*x   |
972*x*|-1 + --------|
      |            2|
      \     2 + 9*x /
---------------------
               2     
     /       2\      
     \2 + 9*x /
$$\frac{972 x \left(\frac{12 x^{2}}{9 x^{2} + 2} - 1\right)}{\left(9 x^{2} + 2\right)^{2}}$$
Simplify
The graph
Derivative of y=ln(9x^2+2)
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