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

Expert Answers
gsarora17 eNotes educator| Certified Educator


Differentiating both sides with respect to x,








Derivative at point (-1,1) can be found by plugging in the values of (x,y) in dy/dx.

Therefore derivative at point (-1,1)=`(-1^2-2(-1)(1))/(1^2+2(-1)(1))`

`Derivative = -1`

` `

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



dy/dx=-1 at any point