Calculus Question And Answer

[mage lang="en|es|en" source="flickr"]calculus question and answer[/mage]
Can u answer this calculus question?

If 1/x + 1/y = 3 and y(4) = 4/11 find y’(4) by implicit differentiation

Just take the equality given and differentiate it
(you can multiply by x*y first to make differentiation a little bit easier):
1/x + 1/y = 3
x*y*(1/x + 1/y )= 3*x*y
y + x = 3xy
(y + x)’ = (3xy)’
y’ + (x)’ = 3*(xy)’
y’ + 1 = 3*((x)’ * y + x*y’)
y’ +1 = 3*(y+x*y’)

Now set x=4:
y’(4) + 1 = 3*(y(4)+4*y’(4))
y’(4) + 1 = 3*(4/11+4*y’(4))
y’(4) + 1 = 12/11+12*y’(4)
11*y’(4) = 1-12/11 = -1/11
y’(4) = -1/121

BC Calculus Sample Question 11 & 12


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One Response
  1. jim says:

    this is awesome man

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