Find dy/dx by implicit differentiation.

Question

(sin 𝜋x + cos 𝜋y)³ = 49

dy/dx = 

 

Answer 1

(sin 𝜋x + cos 𝜋y)³ = 49

3 (sin 𝜋x + cos 𝜋y)² ( 𝜋 cos 𝜋x - 𝜋 sin 𝜋y dy/dx ) = 0

𝜋 cos 𝜋x - 𝜋 sin 𝜋y dy/dx = 0

- 𝜋 sin 𝜋y dy/dx = - 𝜋 cos 𝜋x

dy/dx = cos 𝜋x / sin 𝜋y