`(x + y)^3 = x^3 + y^3, (-1,1)` Find `dy/dx` by implicit differentiation and evaluate the derivative at the given point.

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`(x+y)^3=x^3+y^3`

Differentiating both sides with respect to x,

`3(x+y)^2d/dx(x+y)=3x^2+3y^2dy/dx`

`3(x+y)^2(1+dy/dx)=3x^2+3y^2dy/dx`

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kandukurimaths | Student

given function is

(x + y)3 = x3 + y3

using polynomial identity

(x + y)3 = x3 + 3x2y + 3xy2 + y3

we get

3x2y + 3xy2 =0

3x2y  =- 3xy2

x=-y

y=-x

dy/dx=-1 at any point