The expression you provided, \( \frac{d}{dx} = \frac{2}{x} \), seems to be the derivative of some function. However, you need to specify the function being differentiated. For now, I'll assume you're asking to differentiate \( f(x) = \frac{2}{x} \) with respect to \( x \).

### Solution:

We can rewrite \( \frac{2}{x} \) as \( 2x^{-1} \) to make differentiation easier:

\[
f(x) = 2x^{-1}
\]

Now, applying the power rule for differentiation:

\[
\frac{d}{dx} \left( 2x^{-1} \right) = 2 \cdot (-1) x^{-2} = -\frac{2}{x^2}
\]

### Final Answer:
\[
\frac{d}{dx} \left( \frac{2}{x} \right) = -\frac{2}{x^2}
\]

Would you like further clarification or more details on this process?

### Related questions:
1. How do you apply the power rule in general?
2. What is the chain rule and how does it relate to complex derivatives?
3. How do you differentiate logarithmic functions like \( \ln(x) \)?
4. What happens when you differentiate trigonometric functions like \( \sin(x) \) or \( \cos(x) \)?
5. How can implicit differentiation be used for more complex functions?

### Tip:
Always try to rewrite fractions or roots as powers of \( x \) to simplify differentiation.

Learn how to differentiate the function 2/x using the power rule. This solution demonstrates the step-by-step process, rewriting the function as 2x^(-1) to simplify differentiation. Ideal for students in Grades 11-12 studying pre-calculus or calculus.

Math Problem Statement

Solution

Ask a new question for Free

By Image

Math Problem Analysis

Mathematical Concepts

Formulas

Theorems

Suitable Grade Level

Related Recommendation