litaryl2Mccuspunkel
litaryl2Mccuspunkel litaryl2Mccuspunkel
  • 18-07-2016
  • Mathematics
contestada

How do you implicitly differentiate: sqrt(xy)=x^2y+1

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meerkat18
meerkat18 meerkat18
  • 20-07-2016
Implicit expression refers to equation that are not strictly expressed in terms of y and x separately. In this case, the derivative of expression 
sqrt(xy)=x^2y+1 is

sqrt x * 0.5 y ^-0.5 dy + 
sqrt y * 0.5 x ^-0.5 dx= x^2 dy + 2xy dx 
dy (x^2 - 0.5 (
x/y) ^0.5) = dx (2xy  - 0.5 (y/x)^0.5) 
dy/dx = 
(2xy  - 0.5 (y/x)^0.5) / (x^2 - 0.5 (x/y) ^0.5)
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