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

Answer:

Required relation is $dy=\frac{-12dx}{x^{13}}$.

Step-by-step explanation:

Given,

$f(x)=\frac{1}{x^{12}}$ be such that, $dy=f'(x)dx$.

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

$dy=f'(x)dx$

$=\frac{d}{dx}(f(x))dx$

$=\frac{d}{dx}(x^{-12})dx$

$=-12x^{-12-1}dx$

$\therefore dy=\frac{-12dx}{x^{13}}$

which is the required relation.