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ln(2x^3+3x^2)

Derivative of ln(2x^3+3x^2)

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

The graph:

from to

Piecewise:

The solution

You have entered [src]
   /   3      2\
log\2*x  + 3*x /
$$\log{\left(2 x^{3} + 3 x^{2} \right)}$$
d /   /   3      2\\
--\log\2*x  + 3*x //
dx                  
$$\frac{d}{d x} \log{\left(2 x^{3} + 3 x^{2} \right)}$$
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
The first derivative [src]
          2
 6*x + 6*x 
-----------
   3      2
2*x  + 3*x 
$$\frac{6 x^{2} + 6 x}{2 x^{3} + 3 x^{2}}$$
The second derivative [src]
  /                   2\
  |          6*(1 + x) |
6*|1 + 2*x - ----------|
  \           3 + 2*x  /
------------------------
       2                
      x *(3 + 2*x)      
$$\frac{6 \cdot \left(2 x - \frac{6 \left(x + 1\right)^{2}}{2 x + 3} + 1\right)}{x^{2} \cdot \left(2 x + 3\right)}$$
The third derivative [src]
   /              3                       \
   |    36*(1 + x)     9*(1 + x)*(1 + 2*x)|
12*|1 + ------------ - -------------------|
   |               2       x*(3 + 2*x)    |
   \    x*(3 + 2*x)                       /
-------------------------------------------
                 2                         
                x *(3 + 2*x)               
$$\frac{12 \cdot \left(1 + \frac{36 \left(x + 1\right)^{3}}{x \left(2 x + 3\right)^{2}} - \frac{9 \left(x + 1\right) \left(2 x + 1\right)}{x \left(2 x + 3\right)}\right)}{x^{2} \cdot \left(2 x + 3\right)}$$
The graph
Derivative of ln(2x^3+3x^2)