Mister Exam

Other calculators

The derivative of the function/ ln(3^2-2y^2)

Derivative of ln(3^2-2y^2)

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

The graph:

from to

Piecewise:

The solution

You have entered [src] 
   /       2\
log\9 - 2*y /
$$\log{\left(9 - 2 y^{2} \right)}$$ 
log(9 - 2*y^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 the constant is zero.

      2. 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:

      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*y  
--------
       2
9 - 2*y
$$- \frac{4 y}{9 - 2 y^{2}}$$
Simplify
The second derivative [src] 
  /          2  \
  |       4*y   |
4*|1 - ---------|
  |            2|
  \    -9 + 2*y /
-----------------
            2    
    -9 + 2*y
$$\frac{4 \left(- \frac{4 y^{2}}{2 y^{2} - 9} + 1\right)}{2 y^{2} - 9}$$
Simplify
The third derivative [src] 
     /           2  \
     |        8*y   |
16*y*|-3 + ---------|
     |             2|
     \     -9 + 2*y /
---------------------
                2    
     /        2\     
     \-9 + 2*y /
$$\frac{16 y \left(\frac{8 y^{2}}{2 y^{2} - 9} - 3\right)}{\left(2 y^{2} - 9\right)^{2}}$$
Simplify
    © Mister Exam – Calculator