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y=sinx+1/2cosx

Derivative of y=sinx+1/2cosx

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

The graph:

from to

Piecewise:

The solution

You have entered [src]
         cos(x)
sin(x) + ------
           2   
$$\sin{\left(x \right)} + \frac{\cos{\left(x \right)}}{2}$$
sin(x) + cos(x)/2
Detail solution
  1. Differentiate term by term:

    1. The derivative of sine is cosine:

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

      1. The derivative of cosine is negative sine:

      So, the result is:

    The result is:


The answer is:

The graph
The first derivative [src]
  sin(x)         
- ------ + cos(x)
    2            
$$- \frac{\sin{\left(x \right)}}{2} + \cos{\left(x \right)}$$
The second derivative [src]
 /cos(x)         \
-|------ + sin(x)|
 \  2            /
$$- (\sin{\left(x \right)} + \frac{\cos{\left(x \right)}}{2})$$
The third derivative [src]
sin(x)         
------ - cos(x)
  2            
$$\frac{\sin{\left(x \right)}}{2} - \cos{\left(x \right)}$$
The graph
Derivative of y=sinx+1/2cosx