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Find (dy)/(dx) in the following: (a)x^3...

Find `(dy)/(dx)` in the following:
(a)`x^3+x^2y+x y^2+y^3=81`
(b) `xy+y^2 =tan x+ y `
(c) `x^2 + xy+ y^2 = 100`

Text Solution

Verified by Experts

(a) `x^3+x^2y+xy^2+y^3 = 81`
Differentiating both sides w.r.t. `x`,
`3x^2+2xy+x^2dy/dx+y^2+x(2y)dy/dx+3y^2dy/dx = 0`
`=>dy/dx(x^2+2xy+3y^2) = -(3x^2+2xy+y^2)`
`=>dy/dx = (-(3x^2+2xy+y^2))/(x^2+2xy+3y^2)`

(b)`xy+y^2 = tanx+y`
Differentiating both sides w.r.t. `x`,
...
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