The derivative of \( \frac{2}{x} \) with respect to \( x \) can be calculated using the power rule. First, rewrite the expression:

\[
\frac{2}{x} = 2x^{-1}
\]

Now, apply the power rule to \( 2x^{-1} \):

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

So, the derivative of \( \frac{2}{x} \) is:

\[
-\frac{2}{x^2}
\]

Would you like a more detailed explanation or have any further questions?

Here are 5 related questions:
1. What is the derivative of \( \frac{3}{x} \)?
2. How do you find the derivative of \( \frac{a}{x} \) for any constant \( a \)?
3. Can you explain the power rule in calculus?
4. What is the second derivative of \( \frac{2}{x} \)?
5. How do you differentiate \( \frac{2}{x^2} \)?

**Tip:** Always simplify expressions before differentiating to make the process easier!

Find the derivative of 2/x using the power rule of differentiation. Learn step-by-step how to rewrite 2/x as 2x^(-1) and apply the power rule to obtain -2/x^2. Suitable for students in Grades 11-12.

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