What is implicit (dy)/(dx),(7xy+3)^2=14y ?

The answer to implicit (dy)/(dx),(7xy+3)^2=14y is (dy)/(dx)=-(y(7xy+3))/(7x^2y+3x-1)

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implicit (dy)/(dx),(7xy+3)^2=14y

implicit derivative

\frac{d y}{d x}, (7 x y + 3)^{2} = 14 y

\frac{d y}{d x} = - \frac{y ( 7 x y + 3 )}{7 x ^{2} y + 3 x - 1}

Solution steps

(7 x y + 3)^{2} = 14 y

Treat

y

y (x)

Differentiate both sides:

14 (7 x y + 3) (x \frac{d y}{d x} + y) = 14 \frac{d y}{d x}

Isolate

\frac{d y}{d x} : \frac{d y}{d x} = - \frac{y ( 7 x y + 3 )}{7 x ^{2} y + 3 x - 1}

\frac{d y}{d x} = - \frac{y ( 7 x y + 3 )}{7 x ^{2} y + 3 x - 1}

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\frac{\partial}{\partial x} (\frac{1}{x ^{- 1} + 4 y ^{- 1}})

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\int 729 x^{2} cos (9 x) d x

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

What is implicit (dy)/(dx),(7xy+3)^2=14y ?
The answer to implicit (dy)/(dx),(7xy+3)^2=14y is (dy)/(dx)=-(y(7xy+3))/(7x^2y+3x-1)