Question
Differentiate implicitly (a) x^3+y^3=27xy
Answers
Reiny
x^3+y^3=27xy
I assume you are differentiating with respect to x.
3x^2 + 3y^2 dy/dx = 27x dy/dx + 27y
3y^2 dy/dx - 27x dy/dx = 27y - 3x^2
dy/dx (3y^2 - 27x) = 27y - 3x^2
dy/dx = (27y - 3x^2)/(3y^2 - 27x)
= (9y - x^2)/(y^2 - 9x) or (x^2 - 9y)/(9x - y^2)
check my algebra, did not write it out first
I assume you are differentiating with respect to x.
3x^2 + 3y^2 dy/dx = 27x dy/dx + 27y
3y^2 dy/dx - 27x dy/dx = 27y - 3x^2
dy/dx (3y^2 - 27x) = 27y - 3x^2
dy/dx = (27y - 3x^2)/(3y^2 - 27x)
= (9y - x^2)/(y^2 - 9x) or (x^2 - 9y)/(9x - y^2)
check my algebra, did not write it out first