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log2(sinx)
The derivative of the function/ log2(sinx)

Derivative of log2(sinx)

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

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The solution

You have entered [src] 
log(sin(x))
-----------
   log(2)
log⁡(sin⁡(x))log⁡(2)\frac{\log{\left(\sin{\left(x \right)} \right)}}{\log{\left(2 \right)}} 
d /log(sin(x))\
--|-----------|
dx\   log(2)  /
ddxlog⁡(sin⁡(x))log⁡(2)\frac{d}{d x} \frac{\log{\left(\sin{\left(x \right)} \right)}}{\log{\left(2 \right)}}
Transform
Detail solution

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

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

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

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

      1. The derivative of sine is cosine:

        ddxsin⁡(x)=cos⁡(x)\frac{d}{d x} \sin{\left(x \right)} = \cos{\left(x \right)}

      The result of the chain rule is:

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

    So, the result is: cos⁡(x)log⁡(2)sin⁡(x)\frac{\cos{\left(x \right)}}{\log{\left(2 \right)} \sin{\left(x \right)}}

  2. Now simplify:

    1log⁡(2)tan⁡(x)\frac{1}{\log{\left(2 \right)} \tan{\left(x \right)}}

The answer is:

1log⁡(2)tan⁡(x)\frac{1}{\log{\left(2 \right)} \tan{\left(x \right)}}

The graph
02468-8-6-4-2-1010-500500
Plot the graph f(x)
Plot the graph f'(x)
The first derivative [src] 
    cos(x)   
-------------
log(2)*sin(x)
cos⁡(x)log⁡(2)sin⁡(x)\frac{\cos{\left(x \right)}}{\log{\left(2 \right)} \sin{\left(x \right)}}
Simplify
The second derivative [src] 
 /       2   \ 
 |    cos (x)| 
-|1 + -------| 
 |       2   | 
 \    sin (x)/ 
---------------
     log(2)
−1+cos⁡2(x)sin⁡2(x)log⁡(2)- \frac{1 + \frac{\cos^{2}{\left(x \right)}}{\sin^{2}{\left(x \right)}}}{\log{\left(2 \right)}}
Simplify
The third derivative [src] 
  /       2   \       
  |    cos (x)|       
2*|1 + -------|*cos(x)
  |       2   |       
  \    sin (x)/       
----------------------
    log(2)*sin(x)
2⋅(1+cos⁡2(x)sin⁡2(x))cos⁡(x)log⁡(2)sin⁡(x)\frac{2 \cdot \left(1 + \frac{\cos^{2}{\left(x \right)}}{\sin^{2}{\left(x \right)}}\right) \cos{\left(x \right)}}{\log{\left(2 \right)} \sin{\left(x \right)}}
Simplify
The graph
Derivative of log2(sinx)
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