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ln(3×^2+7×)
The derivative of the function/ ln(3×^2+7×)

Derivative of ln(3×^2+7×)

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

The graph:

from to

Piecewise:

The solution

You have entered [src] 
   /   2      \
log\3*x  + 7*x/
$$\log{\left(3 x^{2} + 7 x \right)}$$ 
log(3*x^2 + 7*x)
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 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] 
 7 + 6*x  
----------
   2      
3*x  + 7*x
$$\frac{6 x + 7}{3 x^{2} + 7 x}$$
Simplify
The second derivative [src] 
              2
     (7 + 6*x) 
6 - -----------
    x*(7 + 3*x)
---------------
  x*(7 + 3*x)
$$\frac{6 - \frac{\left(6 x + 7\right)^{2}}{x \left(3 x + 7\right)}}{x \left(3 x + 7\right)}$$
Simplify
The third derivative [src] 
  /               2\          
  |      (7 + 6*x) |          
2*|-9 + -----------|*(7 + 6*x)
  \     x*(7 + 3*x)/          
------------------------------
         2          2         
        x *(7 + 3*x)
$$\frac{2 \left(-9 + \frac{\left(6 x + 7\right)^{2}}{x \left(3 x + 7\right)}\right) \left(6 x + 7\right)}{x^{2} \left(3 x + 7\right)^{2}}$$
Simplify
The graph
Derivative of ln(3×^2+7×)
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