Find the derivative of 1/x

By Shivank Goel|Updated : August 1st, 2022

The process of determining the derivative is known as differentiation, whereas the inverse process is known as anti-differentiation.

Derivatives are defined as the varying rate of change of a function concerning an independent variable.

The derivative is basically used when there is some varying quantity and the rate of change is not constant.

It is used to measure the sensitivity of one variable (dependent variable) concerning another variable (independent variable).

Derivatives can be classified into various types based on their order, such as first and second-order derivatives.

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We know that the derivative of a function is written as f'(x)

It refers to that the function is a derivative of y concerning the variable x

Consider f(x) = 1/x = x^-1

So by differentiation

f'(x) = n x^{n - 1} , where n = -1

Let us replace the value of n as - 1

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

f'(1/x) = -1/ x²

Therefore, if someone asks you to Find the derivative of 1/x, then the answer will be that the derivative of 1/x is -1/ x²

Summary:

Find the derivative of 1/x.

The derivative of 1/x is -1/ x²

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