What is implicit (dy)/(dx),8x^3+x^2y-xy^3=9 ?

The answer to implicit (dy)/(dx),8x^3+x^2y-xy^3=9 is (dy)/(dx)=(-24x^2-2xy+y^3)/(x(x-3y^2))

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implicit (dy)/(dx),8x^3+x^2y-xy^3=9

implicit derivative

\frac{d y}{d x}, 8 x^{3} + x^{2} y - x y^{3} = 9

\frac{d y}{d x} = \frac{- 24 x ^{2} - 2 x y + y ^{3}}{x ( x - 3 y ^{2} )}

Solution steps

8 x^{3} + x^{2} y - x y^{3} = 9

Treat

y

y (x)

Differentiate both sides:

24 x^{2} + 2 x y + x^{2} \frac{d y}{d x} - y^{3} - 3 x y^{2} \frac{d y}{d x} = 0

Isolate

\frac{d y}{d x} : \frac{d y}{d x} = \frac{- 24 x ^{2} - 2 x y + y ^{3}}{x ( x - 3 y ^{2} )}

\frac{d y}{d x} = \frac{- 24 x ^{2} - 2 x y + y ^{3}}{x ( x - 3 y ^{2} )}

\int \frac{1}{x ^{\frac{4}{5}} ( 1 + x ^{\frac{1}{5}} )} d x

x (\frac{d y}{d x}) = 2 x^{2} + y

f (x) = 7 x + 32, at x = - 1

(x + y) d x + (x + y - 1) d y = 0

\int (\frac{- y}{x ^{2} + y ^{2}}) d x

What is implicit (dy)/(dx),8x^3+x^2y-xy^3=9 ?
The answer to implicit (dy)/(dx),8x^3+x^2y-xy^3=9 is (dy)/(dx)=(-24x^2-2xy+y^3)/(x(x-3y^2))