The function provided is:

\[
f(x) = \sin(x^2) \left( 2x^3 - x - 14 \right)^{\frac{3}{2}}
\]

Let me know what you would like to do with this function. Here are a few possible directions:

1. **Differentiation**: Would you like to compute the derivative \( f'(x) \)?
2. **Integration**: Would you like to compute the integral \( \int f(x) \, dx \)?
3. **Critical points**: Would you like to find the critical points of the function (by setting \( f'(x) = 0 \))?
4. **Limit**: Do you need to evaluate the limit of \( f(x) \) as \( x \to \infty \), or some other point?
5. **Simplification**: Would you like to simplify or reformat the expression?

### Tip:
When working with composite functions like this, applying the chain rule or product rule carefully is essential during differentiation.

Explore how to differentiate the composite function f(x) = sin(x^2)(2x^3 − x − 14)^(3/2). This solution applies key calculus concepts like the chain rule, product rule, and power rule, making it ideal for students in undergraduate calculus courses.

Math Problem Statement

Solution

Ask a new question for Free

By Image

Math Problem Analysis

Mathematical Concepts

Formulas

Theorems

Suitable Grade Level

Related Recommendation