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y=sinx/2*x+16

Derivative of y=sinx/2*x+16

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

The graph:

from to

Piecewise:

The solution

You have entered [src]
sin(x)       
------*x + 16
  2          
$$x \frac{\sin{\left(x \right)}}{2} + 16$$
(sin(x)/2)*x + 16
Detail solution
  1. Differentiate term by term:

    1. Apply the quotient rule, which is:

      and .

      To find :

      1. Apply the product rule:

        ; to find :

        1. Apply the power rule: goes to

        ; to find :

        1. The derivative of sine is cosine:

        The result is:

      To find :

      1. The derivative of the constant is zero.

      Now plug in to the quotient rule:

    2. The derivative of the constant is zero.

    The result is:


The answer is:

The graph
The first derivative [src]
sin(x)   x*cos(x)
------ + --------
  2         2    
$$\frac{x \cos{\left(x \right)}}{2} + \frac{\sin{\left(x \right)}}{2}$$
The second derivative [src]
  x*sin(x)         
- -------- + cos(x)
     2             
$$- \frac{x \sin{\left(x \right)}}{2} + \cos{\left(x \right)}$$
The third derivative [src]
-(3*sin(x) + x*cos(x)) 
-----------------------
           2           
$$- \frac{x \cos{\left(x \right)} + 3 \sin{\left(x \right)}}{2}$$
The graph
Derivative of y=sinx/2*x+16