To find the derivative of the function \( y = -6x^3 \), we'll use the power rule for differentiation. The power rule states that for any term of the form \( ax^n \), the derivative is given by:

\[
\frac{d}{dx}(ax^n) = n \cdot ax^{n-1}
\]

For \( y = -6x^3 \):

1. The coefficient is \(-6\).
2. The exponent is \(3\).

Applying the power rule:

\[
\frac{dy}{dx} = 3 \cdot (-6) \cdot x^{3-1} = -18x^2
\]

So, the derivative of \( y = -6x^3 \) is:

\[
\frac{dy}{dx} = -18x^2
\]

Would you like more details or have any other questions?

Here are five related questions to further your understanding:
1. What is the derivative of \( y = 4x^5 \)?
2. How does the power rule apply to negative exponents?
3. What is the second derivative of \( y = -6x^3 \)?
4. How do you find the derivative of a sum of two terms, like \( y = 3x^4 + 2x^2 \)?
5. What is the derivative of \( y = -6x^3 + 5x \)?

**Tip**: When applying the power rule, always reduce the exponent by one and multiply by the original exponent.

Learn how to find the derivative of y = -6x^3 using the power rule. This solution walks through applying the formula step-by-step, demonstrating how to differentiate polynomial functions. Suitable for Grades 11-12 or college-level calculus students.

Math Problem Statement

Solution

Ask a new question for Free

By Image

Math Problem Analysis

Mathematical Concepts

Formulas

Theorems

Suitable Grade Level

Related Recommendation