What is implicit (dy)/(dx),x^4y-8xy+3xy^2=9 ?

The answer to implicit (dy)/(dx),x^4y-8xy+3xy^2=9 is (dy)/(dx)=(-4x^3y+8y-3y^2)/(x(x^3-8+6y))

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implicit (dy)/(dx),x^4y-8xy+3xy^2=9

implicit derivative

\frac{d y}{d x}, x^{4} y - 8 x y + 3 x y^{2} = 9

\frac{d y}{d x} = \frac{- 4 x ^{3} y + 8 y - 3 y ^{2}}{x ( x ^{3} - 8 + 6 y )}

Solution steps

x^{4} y - 8 x y + 3 x y^{2} = 9

Treat

y

y (x)

Differentiate both sides:

4 x^{3} y + \frac{d y}{d x} x^{4} - 8 (y + x \frac{d y}{d x}) + 3 (y^{2} + 2 x y \frac{d y}{d x}) = 0

Isolate

\frac{d y}{d x} : \frac{d y}{d x} = \frac{- 4 x ^{3} y + 8 y - 3 y ^{2}}{x ( x ^{3} - 8 + 6 y )}

\frac{d y}{d x} = \frac{- 4 x ^{3} y + 8 y - 3 y ^{2}}{x ( x ^{3} - 8 + 6 y )}

x \to 0 lim (\frac{cos ( 3 x - \frac{π}{2} )}{x})

\frac{d}{d x} (ln (cot (5 x)))

f (x) = 4 x^{2} - 4 x + 1

y^{^{''}} + 2 y^{^{'}} + 2 y = sin (x)

\int \frac{1}{2 y - 1} d y

What is implicit (dy)/(dx),x^4y-8xy+3xy^2=9 ?
The answer to implicit (dy)/(dx),x^4y-8xy+3xy^2=9 is (dy)/(dx)=(-4x^3y+8y-3y^2)/(x(x^3-8+6y))