Calculus Question

Question

Find dy/dx if 2x⁵+x⁴y+y⁵ = 36

 

Answer 1

2x⁵ + x⁴y + y⁵ = 36

needs implicit differentiation

 

10x⁴ + [ 4x³y + x⁴(dy/dx) ] + 5y⁴(dy/dx) = 0

x⁴(dy/dx) + 5y⁴(dy/dx) = -10x⁴ - 4x³y 

dy/dx (x⁴ + 5y⁴) = -10x⁴ - 4x³y

dy/dx = (-10x⁴ - 4x³y) / (x⁴ + 5y⁴)