Understanding the Power Rule for Differentiation: Finding the Derivative of 1/x

derivative of 1/x

To find the derivative of the function f(x) = 1/x, we can use the power rule for differentiation

To find the derivative of the function f(x) = 1/x, we can use the power rule for differentiation. The power rule states that if we have a function of the form f(x) = x^n, where n is a constant, the derivative of f(x) with respect to x is given by f'(x) = n * x^(n-1).

In this case, our function is f(x) = 1/x, which can be rewritten as f(x) = x^(-1). Using the power rule, we can differentiate f(x) as follows:

f'(x) = (-1) * x^(-1-1)
= -1 * x^(-2)
= -1/x^2.

Therefore, the derivative of 1/x with respect to x is -1/x^2.

More Answers:

Math Made Easy: Understanding the Antiderivative of e^x using the Power Rule
The Derivative of f(x) = a^x using Logarithmic Differentiation: Simplified Step-by-Step Guide
A Guide to Finding the Antiderivative of a^x: Step-by-Step Explanation and Formula

Share:

Recent Posts

Don't Miss Out! Sign Up Now!

Sign up now to get started for free!