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cos(log(x))
The derivative of the function/ cos(log(x))

Derivative of cos(log(x))

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

The graph:

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Piecewise:

The solution

You have entered [src] 
cos(log(x))
cos⁡(log⁡(x))\cos{\left(\log{\left(x \right)} \right)} 
cos(log(x))
Detail solution

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

  2. The derivative of cosine is negative sine:

    dducos⁡(u)=−sin⁡(u)\frac{d}{d u} \cos{\left(u \right)} = - \sin{\left(u \right)}

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

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

    The result of the chain rule is:

    −sin⁡(log⁡(x))x- \frac{\sin{\left(\log{\left(x \right)} \right)}}{x}

The answer is:

−sin⁡(log⁡(x))x- \frac{\sin{\left(\log{\left(x \right)} \right)}}{x}

The graph
02468-8-6-4-2-1010-1010
Plot the graph f(x)
Plot the graph f'(x)
The first derivative [src] 
-sin(log(x)) 
-------------
      x
−sin⁡(log⁡(x))x- \frac{\sin{\left(\log{\left(x \right)} \right)}}{x}
Simplify
The second derivative [src] 
-cos(log(x)) + sin(log(x))
--------------------------
             2            
            x
sin⁡(log⁡(x))−cos⁡(log⁡(x))x2\frac{\sin{\left(\log{\left(x \right)} \right)} - \cos{\left(\log{\left(x \right)} \right)}}{x^{2}}
Simplify
The third derivative [src] 
-sin(log(x)) + 3*cos(log(x))
----------------------------
              3             
             x
−sin⁡(log⁡(x))+3cos⁡(log⁡(x))x3\frac{- \sin{\left(\log{\left(x \right)} \right)} + 3 \cos{\left(\log{\left(x \right)} \right)}}{x^{3}}
Simplify
The graph
Derivative of cos(log(x))
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