The derivative of \( \sin(2x) \) can be calculated using the chain rule. Here's the step-by-step solution:

1. The derivative of \( \sin(u) \) with respect to \( u \) is \( \cos(u) \).
2. The chain rule tells us to then multiply by the derivative of the inside function, which in this case is \( 2x \). The derivative of \( 2x \) with respect to \( x \) is 2.

So, the derivative of \( \sin(2x) \) is:
\[
\frac{d}{dx} \sin(2x) = 2 \cos(2x)
\]

Would you like more details on how the chain rule is applied here, or do you have any other questions?

Here are 5 related questions to explore further:
1. What is the derivative of \( \cos(2x) \)?
2. How would you differentiate \( \sin(3x) \)?
3. What is the second derivative of \( \sin(2x) \)?
4. Can you find the derivative of \( \sin^2(2x) \)?
5. What is the integral of \( \cos(2x) \)?

**Tip:** The chain rule is crucial when differentiating composite functions. Always differentiate the outer function first and then multiply by the derivative of the inner function.

Explore the derivative of sin(2x) step-by-step using the chain rule. Learn how to apply differentiation techniques to trigonometric functions, such as sin(2x), and understand how to derive the solution 2cos(2x). Ideal for students in Grades 11-12 or those in introductory 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