Find dy/dx by implicit differentiation

Question

(cos 𝜋x + sin 𝜋y)⁶ = 26

Answer 1

(cos(πx)+sin(πy))⁶ = 26

Differentiate both sides

6(cos(πx)+sin(πy))⁵(-sin(πx)π+cos(πy)πdy/dx) = 0

Multiplying the polynomials and Isolating dy/dx

π6cos(πy)dy/dx(cos(πx)+sin(πy))⁵ = 6πsin(πx)(cos(πx)+sin(πy))⁵

Cancelling

cos(πy)dy/dx = sin(πx)

dy/dx = sin(πx)/cos(πy)