https://file.aiquickdraw.com/mathbot/file/1726571209307fdjea8cy.jpg

The derivative of the function \( y = \frac{1 + 2x \sin(5x)}{x} \) with respect to \( x \) is:

\[
\frac{dy}{dx} = 10 \cos(5x) - \frac{1}{x^2}
\]

Would you like any further details on the steps involved?

Here are 5 related questions that could expand your understanding:
1. How can we apply the quotient rule for this differentiation?
2. What is the physical interpretation of a derivative in applied contexts?
3. How would the result change if we had different trigonometric functions?
4. How do we handle higher-order derivatives for this function?
5. What role do chain rules and product rules play in differentiation?

**Tip:** When differentiating trigonometric functions combined with polynomials, always remember to apply both the product rule and chain rule correctly.

Differentiate the function y = (1 + 2x * sin(5x)) / x

Learn how to differentiate the function y = (1 + 2x * sin(5x)) / x step by step. This calculus problem involves the quotient rule, product rule, and chain rule, with applications of trigonometric functions. Suitable for college-level 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