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sin(ln(x))
The derivative of the function/ sin(ln(x))

Derivative of sin(ln(x))

Function f() - derivative -N order at the point
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The graph:

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The solution

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

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

  2. The derivative of sine is cosine:

    ddusin⁡(u)=cos⁡(u)\frac{d}{d u} \sin{\left(u \right)} = \cos{\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:

    cos⁡(log⁡(x))x\frac{\cos{\left(\log{\left(x \right)} \right)}}{x}

The answer is:

cos⁡(log⁡(x))x\frac{\cos{\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] 
cos(log(x))
-----------
     x
cos⁡(log⁡(x))x\frac{\cos{\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] 
3*sin(log(x)) + cos(log(x))
---------------------------
              3            
             x
3sin⁡(log⁡(x))+cos⁡(log⁡(x))x3\frac{3 \sin{\left(\log{\left(x \right)} \right)} + \cos{\left(\log{\left(x \right)} \right)}}{x^{3}}
Simplify
The graph
Derivative of sin(ln(x))
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