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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)
$$\frac{\log{\left(x \right)}}{\log{\left(6 \right)}} + \sin{\left(x \right)}$$ 
log(x)/log(6) + sin(x)
Detail solution

  1. Differentiate 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 is .

      So, the result is:

    2. The derivative of sine is cosine:

    The result is:

The answer is:

The graph
Plot the graph f(x)
Plot the graph f'(x)
The first derivative [src] 
   1             
-------- + cos(x)
x*log(6)
$$\cos{\left(x \right)} + \frac{1}{x \log{\left(6 \right)}}$$
Simplify
The second derivative [src] 
 /    1             \
-|--------- + sin(x)|
 | 2                |
 \x *log(6)         /
$$- (\sin{\left(x \right)} + \frac{1}{x^{2} \log{\left(6 \right)}})$$
Simplify
The third derivative [src] 
              2    
-cos(x) + ---------
           3       
          x *log(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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