How do you differentiate f(x)=1/x^2?

2 Answers
Nov 3, 2016

d/dxf(x) = -2/ x^3

Explanation:

f(x)= 1/x^2
d/dxf(x) =d/dx(1/x^2)
d/dx(1/x^2) = d/dx(x^-2)
implies d/dxf(x) = -2* x^-3
implies d/dxf(x) = -2/ x^3

Nov 3, 2016

dy/dx=(-2)/x^3

Explanation:

Given -

y=1/x^2

Method -1
The given function can be written as -

y=x^-2

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

dy/dx=-2x^-3

dy/dx=(-2)/x^3

Method - 2
We can apply quotient rule

dy/dx={[(x^2)(0)]-[(1)(2x)]}/((x^2)^2)

dy/dx=(-2x)/x^4

dy/dx=(-2)/x^3