Thread: Need help with implicit differentiation

sqrt(5xy) + 2y = y^2 + xy^3

so I got this far and now I am stuck:

d/dx ((5xy)^1/2 + 2y) = d/dx (y^2 + xy^3)

= 1/2(5xy)^1/2-1) Dx(5x) (y) + 5x Dx(y) + 2 Dx(y) = 2y Dx(y) + Dx(x) (y^3) + x (3y^2) Dx (y)

= 1/(2sqrt(5xy)) · 5y + 5x · Dx(y) + 2 · Dx(y) = 2y · Dx(y) + y^3 +3xy^2 · Dx(y)

=?
I'm wondering if I'm doing this right and where would I go from there?

1/(2sqrt(5xy)) · 5y + 5x · Dx(y) + 2 · Dx(y) = 2y · Dx(y) + y^3 +3xy^2 · Dx(y)


The notation is a bit cumbersome but you did a good job

See attachment