Question

If x^3+8xy+y^3=64 , then dy/dx= ?​

Answer 1

Answer:

dy/dx= -(3x^2+ 8y + 3y^2)/8x

Step-by-step explanation:

x^3 + 8xy + y^3 = 64

Differentiate both sides w.r.t. x

3x^2 + 8(x*d/dx y + y*d/dx x) + 3y^2 = 0

3x^2 + 8(x dy/dx + y) + 3y^2 = 0

3x^2 + 8x dy/dx + 8y + 3y^2 = 0

8x dy/dx = -3x^2 - 8y - 3y^2

dy/dx = -3x^2 - 8y - 3y^2/8x

dy/dx = -( 3x^2 + 8y + 3y^2)/8x