Questions: What rule(s) would be performed to take the derivative of y=(2x^3+6x)^4 ? Power Rule Sum Rule Product Rule Quotient Rule Chain Rule Difference Rule Multiplication by constant

Solution Steps

To solve the multiplication problem \(15 \cdot 53\), we can directly use Python to compute the product. For the derivative question, we need to identify which rules apply to the function \(y = (2x^3 + 6x)^4\). The Chain Rule is used because we have a composition of functions, and the Power Rule is used because of the exponent. The Sum Rule is also applicable because the inner function is a sum of terms.

To find the product of \(15\) and \(53\), we perform the multiplication:

\[ 15 \times 53 = 795 \]

For the function \(y = (2x^3 + 6x)^4\), we need to determine which derivative rules apply:

1. Power Rule: This rule is used because the function is raised to the fourth power.
2. Sum Rule: This rule applies because the inner function \(2x^3 + 6x\) is a sum of terms.
3. Chain Rule: This rule is necessary because the function is a composition of an outer function and an inner function.

Final Answer