Question

Consider the following function and express the relationship between a small change in x and the corresponding change in y in the form dy equals f prime (x )dx. f (x )equals StartFraction 1 Over x Superscript 12 EndFraction

Answer 1

Required relation is
`dy=(-12dx)/(x^(13))`.

Explanation:

Given,

`f(x)=(1)/(x^(12))` be such that,
`dy=f'(x)dx`.

To show relationship between a small change in x and corresponding change in y, consider,

`dy=f'(x)dx`

`=(d)/(dx)(f(x))dx`

`=(d)/(dx)(x^(-12))dx`

`=-12x^(-12-1)dx`

`\therefore dy=(-12dx)/(x^(13))`

which is the required relation.