How do we know that the derivative of 1/x is equal to - 1/x^2?

Answer:the derivative of 1/x = -1/x^2

Step-by-step explanation:

1/x can also be written as x^-1

Therefore d/dx of x^-1

=-1*x^-1-1

=-1x^-2

Which can also be written as - 1/x^2

Note: d/dx also means derivative of x

And d/dx (a/x^b) = (a*-b) / x^ (b+1)

Where a and b represents a variable