y=(x^3-6x^2+3x-1)^2/3
2 / 3 2 \ \x - 6*x + 3*x - 1/ ---------------------- 3
/ 2\ |/ 3 2 \ | d |\x - 6*x + 3*x - 1/ | --|----------------------| dx\ 3 /
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:
Apply the power rule: goes to
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 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 derivative of the constant is zero.
The result is:
The result of the chain rule is:
So, the result is:
Now simplify:
The answer is:
/ 2\ / 3 2 \ \6 - 24*x + 6*x /*\x - 6*x + 3*x - 1/ --------------------------------------- 3
/ 2 \ | / 2 \ / 3 2 \| 2*\3*\1 + x - 4*x/ + 2*(-2 + x)*\-1 + x - 6*x + 3*x//
/ 3 2 / 2 \\ 4*\-1 + x - 6*x + 3*x + 9*(-2 + x)*\1 + x - 4*x//