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The derivative of the function/ log2(sqrt3x+4)

Derivative of log2(sqrt3x+4)

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

The graph:

from to

Piecewise:

The solution

You have entered [src] 
   /  _____    \
log\\/ 3*x  + 4/
----------------
     log(2)
$$\frac{\log{\left(\sqrt{3 x} + 4 \right)}}{\log{\left(2 \right)}}$$ 
log(sqrt(3*x) + 4)/log(2)
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. Let .

        2. Apply the power rule: goes to

        3. Then, apply the chain rule. Multiply by :

          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:

          The result of the chain rule is:

        4. The derivative of the constant is zero.

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