Homework SourseFind dydx by implicit differentiation and evaluate the deriv
Find dy/dx by implicit differentiation and evaluate the derivative at the given point.
(2x+2y)^3=(8x^3+8y^3) at (-1,1)
(2x+2y)^3=(8x^3+8y^3) at (-1,1)
Solution
3(2x+2y)^2 (2 + 2dy/dx) = 24x^2 + 24y^2 dy/dx 6(2x+2y)^2 (1 + dy/dx) = 24(x^2+y^2dy/dx) (4x^2 + 4y^2 + 8xy) (1+ y\') = 4x^2 + 4y^2y\' at (-1,1) (4 + 4 -8) (1+y\') = 4 + 4y\' 0 = 4 + 4y\' dy/dx = -1
