anonymous
  • anonymous
find the derivative of f(x) = -3/x at x=-4
Mathematics
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anonymous
  • anonymous
find the derivative of f(x) = -3/x at x=-4
Mathematics
chestercat
  • chestercat
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anonymous
  • anonymous
I got 3/4 but im not sure if that is correct?
dessyj1
  • dessyj1
did you find the derivative of f(x)
anonymous
  • anonymous
How would you do that? Would it be |dw:1434601306329:dw|

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dessyj1
  • dessyj1
no, not quite. You are finding the derivative by using the definition of a derivative. Have you learned the short hand way of finding derivatives by using the the derivative rules?
anonymous
  • anonymous
Would you do the power rule?
dessyj1
  • dessyj1
You would use the quotient rule
anonymous
  • anonymous
I dont know what that is
dessyj1
  • dessyj1
|dw:1434601640378:dw| ring a bell?
dessyj1
  • dessyj1
if it does not that is fine, we can work with the definition of a derivative.
dessyj1
  • dessyj1
|dw:1434601759504:dw| is where you would begin.
anonymous
  • anonymous
oh i just forgot to put it over h
dessyj1
  • dessyj1
then get the numerators to a common denominator
anonymous
  • anonymous
ok so you get (-3/x^2+xh - 3/x^2+xh) / h
anonymous
  • anonymous
which becomes (-6/x^2+xh ) / h ?
dessyj1
  • dessyj1
you forgot to multiply the top by what the value with which you multiplied the bottom
dessyj1
  • dessyj1
at the last step, you were supposed to get ((-3x/x^2+xh)-(-3(x+h)/x^2+xh))/h
dessyj1
  • dessyj1
|dw:1434602235743:dw|
anonymous
  • anonymous
Use L'Hopital's Rule to find derivative, then plug in -4. L'Hopital's Rule: (denominator * derivative of top)- (numerator * derivative of bottom)/(denominator^2) Derivative of -3/x= 3/x^2 Plug in (-4) = 3/16
anonymous
  • anonymous
|dw:1434602370201:dw| |dw:1434602394506:dw|
dessyj1
  • dessyj1
|dw:1434602511993:dw| If you simplified everything correctly you should get
anonymous
  • anonymous
Thanks!!
dessyj1
  • dessyj1
we are not done
dessyj1
  • dessyj1
now you have to cancel out the h and evaluate the limit to find your derivative, or did you use the other guy's method?
dessyj1
  • dessyj1
elysecollinsm=other guy

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