What is implicit (dy)/(dx),3x^2y^3=3x-2y^2-16 ?

The answer to implicit (dy)/(dx),3x^2y^3=3x-2y^2-16 is (dy)/(dx)=(3-6xy^3)/(y(4+9x^2y))

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implicit (dy)/(dx),3x^2y^3=3x-2y^2-16

implicit derivative

\frac{d y}{d x}, 3 x^{2} y^{3} = 3 x - 2 y^{2} - 16

\frac{d y}{d x} = \frac{3 - 6 x y ^{3}}{y ( 4 + 9 x ^{2} y )}

Solution steps

3 x^{2} y^{3} = 3 x - 2 y^{2} - 16

Treat

y

y (x)

Differentiate both sides:

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

Isolate

\frac{d y}{d x} : \frac{d y}{d x} = \frac{3 - 6 x y ^{3}}{y ( 4 + 9 x ^{2} y )}

\frac{d y}{d x} = \frac{3 - 6 x y ^{3}}{y ( 4 + 9 x ^{2} y )}

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

\int \frac{e ^{u}}{( 5 - e ^{u} ) ^{2}} d u

\int \frac{x ^{2} - 25}{x ^{3}} d x

t^{2} y^{^{''}} + 15 t y^{^{'}} + 49 y = 0

f (x) = cot (x) csc (x)

What is implicit (dy)/(dx),3x^2y^3=3x-2y^2-16 ?
The answer to implicit (dy)/(dx),3x^2y^3=3x-2y^2-16 is (dy)/(dx)=(3-6xy^3)/(y(4+9x^2y))