What is implicit (dy)/(dx),(3xy+7)^2=6y ?

The answer to implicit (dy)/(dx),(3xy+7)^2=6y is (dy)/(dx)=-(y(3xy+7))/(3x^2y+7x-1)

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implicit (dy)/(dx),(3xy+7)^2=6y

implicit derivative

\frac{d y}{d x}, (3 x y + 7)^{2} = 6 y

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

Solution steps

(3 x y + 7)^{2} = 6 y

Treat

y

y (x)

Differentiate both sides:

6 (3 x y + 7) (x \frac{d y}{d x} + y) = 6 \frac{d y}{d x}

Isolate

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

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

What is implicit (dy)/(dx),(3xy+7)^2=6y ?
The answer to implicit (dy)/(dx),(3xy+7)^2=6y is (dy)/(dx)=-(y(3xy+7))/(3x^2y+7x-1)