What is implicit (dy)/(dx),x^6-5xy^3=9xy ?

The answer to implicit (dy)/(dx),x^6-5xy^3=9xy is (dy)/(dx)=-(9y-6x^5+5y^3)/(3x(3+5y^2))

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implicit (dy)/(dx),x^6-5xy^3=9xy

implicit derivative

\frac{d y}{d x}, x^{6} - 5 x y^{3} = 9 x y

\frac{d y}{d x} = - \frac{9 y - 6 x ^{5} + 5 y ^{3}}{3 x ( 3 + 5 y ^{2} )}

Solution steps

x^{6} - 5 x y^{3} = 9 x y

Treat

y

y (x)

Differentiate both sides:

6 x^{5} - 5 (y^{3} + 3 x y^{2} \frac{d y}{d x}) = 9 (y + x \frac{d y}{d x})

Isolate

\frac{d y}{d x} : \frac{d y}{d x} = - \frac{9 y - 6 x ^{5} + 5 y ^{3}}{3 x ( 3 + 5 y ^{2} )}

\frac{d y}{d x} = - \frac{9 y - 6 x ^{5} + 5 y ^{3}}{3 x ( 3 + 5 y ^{2} )}

x \to 0 lim (arctan (\frac{1}{x}))

\int \frac{x ^{2} + 2}{x ^{3} ( x + 1 ) ^{3}} d x

\frac{1}{( 1 - 7 x )}, - 6 < x < 0

\frac{\partial}{\partial x} (4 x^{- x^{2} - y^{2} - z^{2}})

\int 7.9 t - 16.6 d t

What is implicit (dy)/(dx),x^6-5xy^3=9xy ?
The answer to implicit (dy)/(dx),x^6-5xy^3=9xy is (dy)/(dx)=-(9y-6x^5+5y^3)/(3x(3+5y^2))