Question

Compute and simplify the derivative of the following functions:

1. g(x)= (7 x-8)
2. f(x)=x² / (x)
3. h(x)=x³ / 3 x² -x¹/³

Answer 1

To find the derivative of a function, use the power rule. Simplify the expressions if possible and then apply the power rule.

Step-by-step explanation:

To find the derivative of a function, we can use the power rule. The power rule states that the derivative of x^n is nx^(n-1), where n is a constant.

1. For g(x)= (7x-8), the derivative is 7.
2. For f(x)=x^2 / x, we can simplify the expression to f(x)=x, and the derivative is 1.
3. For h(x)=x^3 / (3x^2 - x^(1/3)), we can simplify the expression to h(x)=x^3 / (3x^2 - x^(1/3)), and the derivative is [ (3x^2 - x^(1/3)) * (3x^2 - x^(1/3)) * 3 - x^3 * (6x - 1/3x^(-2/3)) ] / (3x^2 - x^(1/3))^2.