What is implicit (dy)/(dx),2xy=6 ?

The answer to implicit (dy)/(dx),2xy=6 is (dy)/(dx)=-y/x

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implicit (dy)/(dx),2xy=6

implicit derivative

\frac{d y}{d x}, 2 x y = 6

\frac{d y}{d x} = - \frac{y}{x}

Solution steps

2 x y = 6

Treat

y

y (x)

Differentiate both sides:

2 (y + x \frac{d y}{d x}) = 0

Isolate

\frac{d y}{d x} : \frac{d y}{d x} = - \frac{y}{x}

\frac{d y}{d x} = - \frac{y}{x}

(8.3) (3.5)

\int (x^{2} + 4)^{5} 3 x d x

\frac{\partial}{\partial x} (5 x^{2} - 3 x y + x yz)

- 2 t^{3}

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

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