Mister Exam

Derivative of (-ln2)cos(logx)²

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

The graph:

from to

Piecewise:

The solution

You have entered [src]
           2        
-log(2)*cos (log(x))
$$- \log{\left(2 \right)} \cos^{2}{\left(\log{\left(x \right)} \right)}$$
d /           2        \
--\-log(2)*cos (log(x))/
dx                      
$$\frac{d}{d x} - \log{\left(2 \right)} \cos^{2}{\left(\log{\left(x \right)} \right)}$$
Detail solution
  1. The derivative of a constant times a function is the constant times the derivative of the function.

    1. Let .

    2. Apply the power rule: goes to

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

      1. Let .

      2. The derivative of cosine is negative sine:

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

        1. The derivative of is .

        The result of the chain rule is:

      The result of the chain rule is:

    So, the result is:

  2. Now simplify:


The answer is:

The graph
The first derivative [src]
2*cos(log(x))*log(2)*sin(log(x))
--------------------------------
               x                
$$\frac{2 \log{\left(2 \right)} \sin{\left(\log{\left(x \right)} \right)} \cos{\left(\log{\left(x \right)} \right)}}{x}$$
The second derivative [src]
   /   2              2                                  \       
-2*\sin (log(x)) - cos (log(x)) + cos(log(x))*sin(log(x))/*log(2)
-----------------------------------------------------------------
                                 2                               
                                x                                
$$- \frac{2 \left(\sin^{2}{\left(\log{\left(x \right)} \right)} + \sin{\left(\log{\left(x \right)} \right)} \cos{\left(\log{\left(x \right)} \right)} - \cos^{2}{\left(\log{\left(x \right)} \right)}\right) \log{\left(2 \right)}}{x^{2}}$$
The third derivative [src]
   /       2                2                                    \       
-2*\- 3*sin (log(x)) + 3*cos (log(x)) + 2*cos(log(x))*sin(log(x))/*log(2)
-------------------------------------------------------------------------
                                     3                                   
                                    x                                    
$$- \frac{2 \left(- 3 \sin^{2}{\left(\log{\left(x \right)} \right)} + 2 \sin{\left(\log{\left(x \right)} \right)} \cos{\left(\log{\left(x \right)} \right)} + 3 \cos^{2}{\left(\log{\left(x \right)} \right)}\right) \log{\left(2 \right)}}{x^{3}}$$
The graph
Derivative of (-ln2)cos(logx)²