1 What is the derivative?
Are you looking to find out the derivative of 1 x? If yes, then you are on the right page. But, before we let you know the answer to this math question, let’s first get to know what exactly is the meaning of derivative.
Derivative is the rate of change of a function with respect to a variable. Derivatives are indispensable to solve the problems in differential equations and is considered an essential tool for calculus.
2 What is the derivative of a function?
As you want to know what is the derivative of 1/x, it is vital to know what does derivative of function mean.
The derivative of a function y=f(x) of a variable x is a measure of the rate at which the value y of the function changes with respect to the change of the variable x. If the graph of f is plotted against x (considering x and y are real numbers), the derivative is the slope of the graph at each point.
1/x can be written as x-1
Using the power rule which states that ddx[xn]=nxn-1
= d/dx 1/x
= d/dx x-1
[d/dx xn= nxn-1]
= -1 x-2