Question

What is the derivative of `x^2/5`?

Answer 1

`(df)/(dx)=2/5x`

Explanation:

AS `f(x)=x^2/5`

`f(x+h)=(x+h)^2/5=(x^2+2hx+h^2)/5=x^2/5+2/5hx+h^2/5`

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

= `Lt_(h->0)(x^2/5+2/5hx+h^2/5-x^2/5)/h`

= `Lt_(h->0)(2/5hx+h^2/5)/h`

= `Lt_(h->0)(2/5x+h/5)`

= `2/5x`