What is the derivative of 1/x?
Given
- Function = 1/x
- Rewrite using power form
Step 1: Rewrite the Function in Power Form
First, rewrite the given function in power form:
1/x = x−1
Step 2: Use the Power Rule of Differentiation
The power rule states:
d/dx (xn) = n xn − 1
Step 3: Differentiate x−1
Here, the power of x is −1.
d/dx (x−1) = −1 · x−2
Step 4: Rewrite the Answer in Fractional Form
−x−2 = −1/x2
Final Answer
d/dx (1/x) = −1/x2