_____ ______________ 3*\/ 2*x + 5*\/ 2*6800 - 2*x
d / _____ ______________\ --\3*\/ 2*x + 5*\/ 2*6800 - 2*x / dx
Differentiate term by term:
The derivative of a constant times a function is the constant times the derivative of the function.
Let .
Apply the power rule: goes to
Then, apply the chain rule. Multiply by :
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:
The result of the chain rule is:
So, the result is:
The derivative of a constant times a function is the constant times the derivative of the function.
Let .
Apply the power rule: goes to
Then, apply the chain rule. Multiply by :
Differentiate term by term:
The derivative of the constant is zero.
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 is:
The result of the chain rule is:
So, the result is:
The result is:
Now simplify:
The answer is:
___ 5 3*\/ 2 - ---------------- + ------- ______________ ___ \/ 2*6800 - 2*x 2*\/ x
___ / 3 5 \ -\/ 2 *|---- + -------------| | 3/2 3/2| \x (6800 - x) / ------------------------------ 4
___ / 5 3 \ 3*\/ 2 *|- ------------- + ----| | 5/2 5/2| \ (6800 - x) x / -------------------------------- 8