Final answer:
The function y = x³ - 3/2x² can typically be differentiated using the power rule, which simplifies to y' = 3x² - 3/x². Differentiating from first principles would involve the limit definition of the derivative, which may be more advanced for high school students.
Step-by-step explanation:
Differentiation from First Principles
The method of differentiating a function from first principles entails applying the fundamental definition of the derivative, which is the limit of the average rate of change of the function as the interval approaches zero. To differentiate the given function y = x³ - 3/2x², one would ordinarily use the derivative function limit:
lim ∈x→0 [f(x+∈x) - f(x)]/∈x
However, due to potential calculation complexity and student's level, it's usually more appropriate at the high school level to utilize derivative rules such as the power rule, the quotient rule, or the product rule. For y = x³ - 3/2x², you would apply the power rule to find y', the first derivative.
The derivative, using the power rule, is:
y' = 3x² - 3/x²
This simplifies the calculation significantly compared to computing it from first principles.