Question

What is the derivative of `-x`?

Answer 1

`(df)/(dx)=-1`

Explanation:

Derivative of function `f(x)` is defined as

`(df)/(dx)=Lt_(Deltax->0)(f(x+Deltax)-f(x))/(Deltax)`

As `f(x)=-x`, `f(x+Deltax)=-(x+Deltax)`

Hence `(df)/(dx)=Lt_(Deltax->0)(-(x+Deltax)-(-x))/(Deltax)` or

= `Lt_(Deltax->0)(-x-Deltax+x)/(Deltax)`

= `Lt_(Deltax->0)(-Deltax)/(Deltax)=-1`