Find the derivative of the function.
-$$y = \frac { x ^ { 3 } } { x - 1 }$$
A) $y ^ { \prime } = \frac { - 2 x ^ { 3 } - 3 x ^ { 2 } } { ( x - 1 ) ^ { 2 } }$
B) $y ^ { \prime } = \frac { - 2 x ^ { 3 } + 3 x ^ { 2 } } { ( x - 1 ) ^ { 2 } }$
C) $y ^ { \prime } = \frac { 2 x ^ { 3 } - 3 x ^ { 2 } } { ( x - 1 ) ^ { 2 } }$
D) $y ^ { \prime } = \frac { 2 x ^ { 3 } + 3 x ^ { 2 } } { ( x - 1 ) ^ { 2 } }$

Question

Quizplus · Accepted Answer

We can use the quotient rule to find the derivative of the function. Let f(x) = x^3 and g(x) = x - 1. Then, 
f'(x) = 3x^2 and g'(x) = 1. Applying the quotient rule, we get
y' = (f'(x)g(x) - f(x)g'(x))/(g(x))^2
y' = [(3x^2)(x - 1) - (x^3)(1)]/(x - 1)^2
y' = (2x^3 - 3x^2)/(x - 1)^2
Therefore, the correct choice is C.

Find the Derivative of the Function y=x3x−1y = \frac { x ^ { 3 } } { x - 1 }y=x−1x3​

Find the Derivative of the Function $y = \frac { x ^ { 3 } } { x - 1 }$