Implicit expression refers to equation that are not strictly expressed in terms of y and x separately. In this case, the derivative of expression
<span>sqrt(xy)=x^2y+1 is
sqrt x * 0.5 y ^-0.5 dy + </span>sqrt y<span> * 0.5 x ^-0.5 dx= x^2 dy + 2xy dx
dy (x^2 - 0.5 (</span>x/y) ^0.5) = dx (2xy - 0.5 (y<span>/x)^0.5)
dy/dx = </span>(2xy - 0.5 (y/x)^0.5) / (x^2 - 0.5 (<span>x/y) ^0.5)</span>
[ - 6 * x^2 * y^8 + 12* x * y^3 - 36 * x * y^2 ] / [6*x*y^2] =
[-6x^2 y^8 ] / [6xy^2] + [12x y^3] / [6xy^2] - [36xy^2] / [6xy^2] =
- xy^6 + 2y - 6
Answer: - xy^6 + 2y - 6
No one is going to be a great way to start a
