`(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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gsarora17
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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
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