Mister Exam

Other calculators

The derivative of the function/ log(x^2+x,2)

Derivative of log(x^2+x,2)

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

The graph:

from to

Piecewise:

The solution

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

        2. Apply the power rule: goes to

        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] 
    1 + 2*x    
---------------
/ 2    \       
\x  + x/*log(2)
$$\frac{2 x + 1}{\left(x^{2} + x\right) \log{\left(2 \right)}}$$
Simplify
The second derivative [src] 
              2 
     (1 + 2*x)  
 2 - ---------- 
     x*(1 + x)  
----------------
x*(1 + x)*log(2)
$$\frac{2 - \frac{\left(2 x + 1\right)^{2}}{x \left(x + 1\right)}}{x \left(x + 1\right) \log{\left(2 \right)}}$$
Simplify
The third derivative [src] 
             /             2\
             |    (1 + 2*x) |
-2*(1 + 2*x)*|3 - ----------|
             \    x*(1 + x) /
-----------------------------
       2        2            
      x *(1 + x) *log(2)
$$- \frac{2 \left(3 - \frac{\left(2 x + 1\right)^{2}}{x \left(x + 1\right)}\right) \left(2 x + 1\right)}{x^{2} \left(x + 1\right)^{2} \log{\left(2 \right)}}$$
Simplify
    © Mister Exam – Calculator