Derivatives of products and quotients Find the derivative of the following functions by first expanding or simplifying the expression. Simplify your answers. 
y = 12s³-8s²+12s/4s

Verified step by step guidance

1. Step 1: Begin by simplifying the expression \( y = \frac{12s^3 - 8s^2 + 12s}{4s} \). This involves dividing each term in the numerator by the denominator \( 4s \).
2. Step 2: Simplify each term separately: \( \frac{12s^3}{4s} = 3s^2 \), \( \frac{-8s^2}{4s} = -2s \), and \( \frac{12s}{4s} = 3 \).
3. Step 3: Rewrite the simplified expression as \( y = 3s^2 - 2s + 3 \).
4. Step 4: Differentiate the simplified expression term by term. Use the power rule \( \frac{d}{ds}[s^n] = ns^{n-1} \) for each term.
5. Step 5: Apply the power rule: The derivative of \( 3s^2 \) is \( 6s \), the derivative of \( -2s \) is \( -2 \), and the derivative of \( 3 \) is \( 0 \). Combine these to find the derivative of the function.