Find the derivative of f(x) = 2/x at x = -2.

Question

anonymous · Answer

-1/2

anonymous · Answer

$$f \prime(x) = \frac{ -2 }{ x^2 }$$ then plug in x...

mathmale · Answer

@Jesi:  Please provide guidance to the person asking the question so that that person may find his or her own answers.  This is an overriding rule in OpenStudy.  Do not just provide answers with no involvement on the part of the person asking the question.

anonymous · Answer

lol. So when they are set up in fractions you could always find it by adding ^2 to x?

anonymous · Answer

sorry...

anonymous · Answer

@yesy7 you can use the idea of negative exponents... :)

anonymous · Answer

Oh, okay. Thank you!!

mathmale · Answer

"So when they are set up in fractions you could always find it by adding ^2 to x?"  No.  You need to know how to apply the Power Rule for Differentiation in this case.

You'd find this easier if you'd rewrite the given function as $$f(x)=2x ^{-1}$$ and then apply the power rule to that.

Can you do that? 

What is $$\frac{ d }{ dx }x ^{-1}?$$

mathmale · Answer

Please note:  You must know the Power Rule (along with a good number of other rules for differentiation):$$\frac{ d }{ dx }x^n=nx ^{n-1}$$

mathmale · Answer

In$$\frac{ d }{ dx }x ^{-1},~n=-1$$