Find dy/dx in terms of x and y if arcsin(x^5y)=xy^5.

Answer 1

arcsin(x^5y) = xy^5
1/√(1-x^10y^2) * (5x^4y + x^5 y') = y^5 + 5xy^4 y'

y' =
y^5 - 5x^4y/√(1-x^10y^2)
--------------------------
x^5/√(1-x^10y^2) - 5xy^4

you can massage that if you want to get rid of the fractions