How do you find the derivitive of f(x) = 2/x?

Answer 1

If you are at the point in your course where you are using differentiation rules, then the best way to handle reciprocals is to use negative exponents.

f(x) = 2x^(-1).

Then use the power rule.

If you are taking derivatives using the definition of the derivative as a limit, you need to simplify the quotient

[ 2/(x+h) - 2/x]/h

this is done most easily by multiplying top and bottom by
(x+h)x and noting all the cancellations.

Answer 2

I'm not sure of which way you know, so I'll show you the short way I know.

You agree that f(x) = 2/x = 2x ^ -1

And that to find the derivative of ax ^ b, you do this:

b * ax ^ (b-1)

So to find your derivative, you do this:

-1 * 2x ^ (-1 - 1)

which equals

-2x ^ -2 or -2/(x ^ 2)

Remember: if you have a variable in the denominator, make it a negative exponent! The process will be much easier if you do.

Answer 3

derivative will be -2/x^2