What is The Derivative of 1/x

Answer: We can express 1 / x as x^-1.

We know that (as per the power rule), If x is a variable and n is the power, then the derivative of x raised to the power n can be written as:

d / dx(xⁿ)=nx^n-1 

Hence,

d / dx(x^-1)=-1 (x^-1-1)

d / dx(x^-1)=-1 (x^-2)

d / dx(x^-1)= –1 / x²

Therefore, the derivative of 1 / x is –1 / x².