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y=lg(10x^2+7)

Derivative of y=lg(10x^2+7)

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

The graph:

from to

Piecewise:

The solution

You have entered [src]
   /    2    \
log\10*x  + 7/
$$\log{\left(10 x^{2} + 7 \right)}$$
log(10*x^2 + 7)
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
The first derivative [src]
   20*x  
---------
    2    
10*x  + 7
$$\frac{20 x}{10 x^{2} + 7}$$
The second derivative [src]
   /          2  \
   |      20*x   |
20*|1 - ---------|
   |            2|
   \    7 + 10*x /
------------------
            2     
    7 + 10*x      
$$\frac{20 \left(- \frac{20 x^{2}}{10 x^{2} + 7} + 1\right)}{10 x^{2} + 7}$$
The third derivative [src]
      /           2  \
      |       40*x   |
400*x*|-3 + ---------|
      |             2|
      \     7 + 10*x /
----------------------
                2     
     /        2\      
     \7 + 10*x /      
$$\frac{400 x \left(\frac{40 x^{2}}{10 x^{2} + 7} - 3\right)}{\left(10 x^{2} + 7\right)^{2}}$$
The graph
Derivative of y=lg(10x^2+7)