Mister Exam

Derivative of 3log2(x)(4x+5)-6x

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

The graph:

from to

Piecewise:

The solution

You have entered [src]
  log(x)                
3*------*(4*x + 5) - 6*x
  log(2)                
$$- 6 x + 3 \frac{\log{\left(x \right)}}{\log{\left(2 \right)}} \left(4 x + 5\right)$$
(3*(log(x)/log(2)))*(4*x + 5) - 6*x
Detail solution
  1. Differentiate term by term:

    1. Apply the quotient rule, which is:

      and .

      To find :

      1. The derivative of a constant times a function is the constant times the derivative of the function.

        1. Apply the product rule:

          ; to find :

          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:

          ; to find :

          1. The derivative of is .

          The result is:

        So, the result is:

      To find :

      1. The derivative of the constant is zero.

      Now plug in to the quotient rule:

    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:

  2. Now simplify:


The answer is:

The graph
The first derivative [src]
     12*log(x)   3*(4*x + 5)
-6 + --------- + -----------
       log(2)      x*log(2) 
$$\frac{12 \log{\left(x \right)}}{\log{\left(2 \right)}} - 6 + \frac{3 \left(4 x + 5\right)}{x \log{\left(2 \right)}}$$
The second derivative [src]
  /    5 + 4*x\
3*|8 - -------|
  \       x   /
---------------
    x*log(2)   
$$\frac{3 \left(8 - \frac{4 x + 5}{x}\right)}{x \log{\left(2 \right)}}$$
The third derivative [src]
  /     5 + 4*x\
6*|-6 + -------|
  \        x   /
----------------
    2           
   x *log(2)    
$$\frac{6 \left(-6 + \frac{4 x + 5}{x}\right)}{x^{2} \log{\left(2 \right)}}$$