Question

First derivative of b/x ​

Answer 1

`(dy)/(dx) = -(b)/(x^2)`

Explanation:

Given

`(b)/(x)`

Required

Determine the first derivative

Rewrite the expression as:

`y =(b)/(x)`

Apply law of indices

`y =bx^(-1)`

An equation with the form

`y = ax^n`

has the derivative:

`(dy)/(dx) = nax^(n-1)`

So, the derivative of
`y =bx^(-1)` is

`(dy)/(dx) = -1 * bx^(-1-1)`

`(dy)/(dx) = -bx^(-2)`

`(dy)/(dx) = -(b)/(x^2)`