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y=log5(3x^2-5)

Derivative of y=log5(3x^2-5)

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

The graph:

from to

Piecewise:

The solution

You have entered [src]
   /   2    \
log\3*x  - 5/
-------------
    log(5)   
$$\frac{\log{\left(3 x^{2} - 5 \right)}}{\log{\left(5 \right)}}$$
  /   /   2    \\
d |log\3*x  - 5/|
--|-------------|
dx\    log(5)   /
$$\frac{d}{d x} \frac{\log{\left(3 x^{2} - 5 \right)}}{\log{\left(5 \right)}}$$
Detail solution
  1. The derivative of a constant times a function is the constant times the derivative of the function.

    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:

    So, the result is:

  2. Now simplify:


The answer is:

The graph
The first derivative [src]
       6*x       
-----------------
/   2    \       
\3*x  - 5/*log(5)
$$\frac{6 x}{\left(3 x^{2} - 5\right) \log{\left(5 \right)}}$$
The second derivative [src]
   /           2  \
   |        6*x   |
-6*|-1 + ---------|
   |             2|
   \     -5 + 3*x /
-------------------
 /        2\       
 \-5 + 3*x /*log(5)
$$- \frac{6 \cdot \left(\frac{6 x^{2}}{3 x^{2} - 5} - 1\right)}{\left(3 x^{2} - 5\right) \log{\left(5 \right)}}$$
The third derivative [src]
      /           2  \
      |        4*x   |
108*x*|-1 + ---------|
      |             2|
      \     -5 + 3*x /
----------------------
            2         
 /        2\          
 \-5 + 3*x / *log(5)  
$$\frac{108 x \left(\frac{4 x^{2}}{3 x^{2} - 5} - 1\right)}{\left(3 x^{2} - 5\right)^{2} \log{\left(5 \right)}}$$
The graph
Derivative of y=log5(3x^2-5)