What is implicit (dy)/(dx),xy-6=0 ?

The answer to implicit (dy)/(dx),xy-6=0 is (dy)/(dx)=-y/x

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implicit (dy)/(dx),xy-6=0

implicit derivative

\frac{d y}{d x}, x y - 6 = 0

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

Solution steps

x y - 6 = 0

Treat

y

y (x)

Differentiate both sides:

x \frac{d y}{d x} + y = 0

Isolate

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

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

\int 2 sin^{3} (5 x) cos^{3} (5 x) d x

\frac{\partial}{\partial x} (sin^{3} (x^{2} y))

\frac{d y}{d x} + 3 y x^{3} = 0

\int t^{2} sin (n t) d t

What is implicit (dy)/(dx),xy-6=0 ?
The answer to implicit (dy)/(dx),xy-6=0 is (dy)/(dx)=-y/x