Question

find dy/dx, if y=x power 3 +3xy +y power 3?​

Answer 1

Answer:

dy/dx = (3x² + 3y)/(1- 3x + 3y²)

Step-by-step explanation:

y = x³ + 3xy + y³

Diff. w. r. t. x

dy/dx = 3x² + 3y + 3x. dy/dx  + 3y² . dy/dx

dy/dx = 3x² + 3y  + (3x + 3y²)(dy/dx)

dy/dx - (3x + 3y²)(dy/dx) = 3x² + 3y

Take dy/dx common:

dy/dx(1 - 3x + 3y²) = 3x² + 3y

dy/dx = (3x² + 3y)/(1- 3x + 3y²)

Answer 2

The question-

Find dy/dx, if y=x power 3 +3xy +y power 3?

Explanation-

y = x³+3xy+y³

so,

dy/dx = 3xy²d/dx (implict differentiation)

= 3y²

Final Answer - 3y²