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ln(4x^2+x)
The derivative of the function/ ln(4x^2+x)

Derivative of ln(4x^2+x)

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

The graph:

from to

Piecewise:

The solution

You have entered [src] 
   /   2    \
log\4*x  + x/
$$\log{\left(4 x^{2} + x \right)}$$ 
d /   /   2    \\
--\log\4*x  + x//
dx
$$\frac{d}{d x} \log{\left(4 x^{2} + x \right)}$$
Transform
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. Apply the power rule: goes to

      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] 
1 + 8*x 
--------
   2    
4*x  + x
$$\frac{8 x + 1}{4 x^{2} + x}$$
Simplify
The second derivative [src] 
              2
     (1 + 8*x) 
8 - -----------
    x*(1 + 4*x)
---------------
  x*(1 + 4*x)
$$\frac{8 - \frac{\left(8 x + 1\right)^{2}}{x \left(4 x + 1\right)}}{x \left(4 x + 1\right)}$$
Simplify
The third derivative [src] 
            /                2\
            |       (1 + 8*x) |
2*(1 + 8*x)*|-12 + -----------|
            \      x*(1 + 4*x)/
-------------------------------
          2          2         
         x *(1 + 4*x)
$$\frac{2 \left(-12 + \frac{\left(8 x + 1\right)^{2}}{x \left(4 x + 1\right)}\right) \left(8 x + 1\right)}{x^{2} \left(4 x + 1\right)^{2}}$$
Simplify
The graph
Derivative of ln(4x^2+x)
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