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y=log6(x)+sinx
The derivative of the function/ y=log6(x)+sinx

Derivative of y=log6(x)+sinx

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

The graph:

from to

Piecewise:

The solution

You have entered [src] 
log(x)         
------ + sin(x)
log(6)
log⁡(x)log⁡(6)+sin⁡(x)\frac{\log{\left(x \right)}}{\log{\left(6 \right)}} + \sin{\left(x \right)} 
log(x)/log(6) + sin(x)
Detail solution

  1. Differentiate log⁡(x)log⁡(6)+sin⁡(x)\frac{\log{\left(x \right)}}{\log{\left(6 \right)}} + \sin{\left(x \right)} term by term:

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

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

      So, the result is: 1xlog⁡(6)\frac{1}{x \log{\left(6 \right)}}

    2. The derivative of sine is cosine:

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

    The result is: cos⁡(x)+1xlog⁡(6)\cos{\left(x \right)} + \frac{1}{x \log{\left(6 \right)}}

The answer is:

cos⁡(x)+1xlog⁡(6)\cos{\left(x \right)} + \frac{1}{x \log{\left(6 \right)}}

The graph
02468-8-6-4-2-1010-1010
Plot the graph f(x)
Plot the graph f'(x)
The first derivative [src] 
   1             
-------- + cos(x)
x*log(6)
cos⁡(x)+1xlog⁡(6)\cos{\left(x \right)} + \frac{1}{x \log{\left(6 \right)}}
Simplify
The second derivative [src] 
 /    1             \
-|--------- + sin(x)|
 | 2                |
 \x *log(6)         /
−(sin⁡(x)+1x2log⁡(6))- (\sin{\left(x \right)} + \frac{1}{x^{2} \log{\left(6 \right)}})
Simplify
The third derivative [src] 
              2    
-cos(x) + ---------
           3       
          x *log(6)
−cos⁡(x)+2x3log⁡(6)- \cos{\left(x \right)} + \frac{2}{x^{3} \log{\left(6 \right)}}
Simplify
The graph
Derivative of y=log6(x)+sinx
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