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The derivative of the function/ log10(x^2-3x)

Derivative of log10(x^2-3x)

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

The graph:

from to

Piecewise:

The solution

You have entered [src] 
   / 2      \
log\x  - 3*x/
-------------
   log(10)
$$\frac{\log{\left(x^{2} - 3 x \right)}}{\log{\left(10 \right)}}$$ 
log(x^2 - 3*x)/log(10)
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. Apply the power rule: goes to

        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:

    So, the result is:

  2. Now simplify:

The answer is:

The graph
Plot the graph f(x)
Plot the graph f'(x)
The first derivative [src] 
     -3 + 2*x     
------------------
/ 2      \        
\x  - 3*x/*log(10)
$$\frac{2 x - 3}{\left(x^{2} - 3 x\right) \log{\left(10 \right)}}$$
Simplify
The second derivative [src] 
               2  
     (-3 + 2*x)   
 2 - -----------  
      x*(-3 + x)  
------------------
x*(-3 + x)*log(10)
$$\frac{2 - \frac{\left(2 x - 3\right)^{2}}{x \left(x - 3\right)}}{x \left(x - 3\right) \log{\left(10 \right)}}$$
Simplify
The third derivative [src] 
              /              2\
              |    (-3 + 2*x) |
-2*(-3 + 2*x)*|3 - -----------|
              \     x*(-3 + x)/
-------------------------------
       2         2             
      x *(-3 + x) *log(10)
$$- \frac{2 \left(3 - \frac{\left(2 x - 3\right)^{2}}{x \left(x - 3\right)}\right) \left(2 x - 3\right)}{x^{2} \left(x - 3\right)^{2} \log{\left(10 \right)}}$$
Simplify
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