Question

does anyone know how to get this?

determine the slope of the following curve at the given point

2xy^(1/3)+4y=12;(4,1)

Answer 1

I assume this is calculus.
You have to solve this implicitly.

differenrtiate both sides of the equation with respect to x.
get terms with dy/dx on left side (my preference is the left side), move all other terms to the other side.
facator dy/dx out of the left side.
then solve for dy/dx.

dont forget your product rule for 2xy^1/3

Answer 2

then when you solved for dy/dx you can plug in your points