How do you use implicit differentiation to find #(dy)/(dx)# given #5x^3=-3xy+2#?
For -3xy the product rule states f g' + f' g
Say -3x is f and y is g
-3x y' + -3 y
When you differentiate, especially implicit differentiation, you follow what the rules say, and this one is saying
Differentiate each term with respect to
the first term on the RHS is differentiated using the product rule
cancel the 3 out.