/pi*x\ -pi*sin|----| \ 4 / ------------- - 20 4
((-pi)*sin((pi*x)/4))/4 - 20
Differentiate term by term:
The derivative of a constant times a function is the constant times the derivative of the function.
The derivative of a constant times a function is the constant times the derivative of the function.
Let .
The derivative of sine is cosine:
Then, apply the chain rule. Multiply by :
The derivative of a constant times a function is the constant times the derivative of the function.
The derivative of a constant times a function is the constant times the derivative of the function.
Apply the power rule: goes to
So, the result is:
So, the result is:
The result of the chain rule is:
So, the result is:
So, the result is:
The derivative of the constant is zero.
The result is:
Now simplify:
The answer is:
2 /pi*x\ -pi *cos|----| \ 4 / --------------- 16
3 /pi*x\ pi *sin|----| \ 4 / ------------- 64