Question

What is the Derivative of f(x)=1/X?
Would it be X^-1?

Answer 1

-x^-2

Answer 2

Write \[f(x)={1\over x} =x^{-1}\]Now just use the exponent rule.

As Nameo0 just said, this is equal to \[-1 * x^{-2} = -{1\over x^2}\]

Answer 3

Thank you ;-)

Answer 4

Ok so then if I need to compelete a table I would use
\[-x^{-2}\left( dx\right)\] to find dy?

example if x=4 and dx = 1.000 then I have
\[-4^{-2}\left( 1.000\right)\] =-.0625?

and if my dx=delta(x)
And use f(x+dx)-f(x)
which would be
\[4^{-1}+1.000-4^{-1}=1.000\] for delta y?