Question

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

Answer 1

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)