Find dy/dx by implicit differentiation

Question

2/y + 4/x= 1

dy/dx=?

Answer 1

2 / y + 4 / x = 1

Apply derivative to each side

power : d / dx(xⁿ) = nx^n-1

2(-1 / y²) dy / dx + 4(-1 / x²) = 0

Divide each side by negitive 2

(1 / y²)dy / dx + 2 / x² = 0

(1 / y²)dy / dx = -2 / x²

Simplify

Therefore dy / dx = -2y² / x² .