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The derivative of the function/ y=cos*1/log2x

Derivative of y=cos*1/log2x

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

The graph:

from to

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The solution

You have entered [src] 
 cos(1) 
--------
log(2*x)
cos⁡(1)log⁡(2x)\frac{\cos{\left(1 \right)}}{\log{\left(2 x \right)}} 
cos(1)/log(2*x)
Detail solution

  1. The derivative of a constant times a function is the constant times the derivative of the function.

    1. Let u=log⁡(2x)u = \log{\left(2 x \right)}.

    2. Apply the power rule: 1u\frac{1}{u} goes to −1u2- \frac{1}{u^{2}}

    3. Then, apply the chain rule. Multiply by ddxlog⁡(2x)\frac{d}{d x} \log{\left(2 x \right)}:

      1. Let u=2xu = 2 x.

      2. The derivative of log⁡(u)\log{\left(u \right)} is 1u\frac{1}{u}.

      3. Then, apply the chain rule. Multiply by ddx2x\frac{d}{d x} 2 x:

        1. The derivative of a constant times a function is the constant times the derivative of the function.

          1. Apply the power rule: xx goes to 11

          So, the result is: 22

        The result of the chain rule is:

        1x\frac{1}{x}

      The result of the chain rule is:

      −1xlog⁡(2x)2- \frac{1}{x \log{\left(2 x \right)}^{2}}

    So, the result is: −cos⁡(1)xlog⁡(2x)2- \frac{\cos{\left(1 \right)}}{x \log{\left(2 x \right)}^{2}}

The answer is:

−cos⁡(1)xlog⁡(2x)2- \frac{\cos{\left(1 \right)}}{x \log{\left(2 x \right)}^{2}}

The graph
02468-8-6-4-2-1010-2000010000
Plot the graph f(x)
Plot the graph f'(x)
The first derivative [src] 
  -cos(1)  
-----------
     2     
x*log (2*x)
−cos⁡(1)xlog⁡(2x)2- \frac{\cos{\left(1 \right)}}{x \log{\left(2 x \right)}^{2}}
Simplify
The second derivative [src] 
/       2    \       
|1 + --------|*cos(1)
\    log(2*x)/       
---------------------
      2    2         
     x *log (2*x)
(1+2log⁡(2x))cos⁡(1)x2log⁡(2x)2\frac{\left(1 + \frac{2}{\log{\left(2 x \right)}}\right) \cos{\left(1 \right)}}{x^{2} \log{\left(2 x \right)}^{2}}
Simplify
The third derivative [src] 
   /       3           3    \       
-2*|1 + -------- + ---------|*cos(1)
   |    log(2*x)      2     |       
   \               log (2*x)/       
------------------------------------
             3    2                 
            x *log (2*x)
−2(1+3log⁡(2x)+3log⁡(2x)2)cos⁡(1)x3log⁡(2x)2- \frac{2 \left(1 + \frac{3}{\log{\left(2 x \right)}} + \frac{3}{\log{\left(2 x \right)}^{2}}\right) \cos{\left(1 \right)}}{x^{3} \log{\left(2 x \right)}^{2}}
Simplify
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