What is implicit (dy)/(dx),4xy=8 ?

The answer to implicit (dy)/(dx),4xy=8 is (dy)/(dx)=-y/x

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implicit (dy)/(dx),4xy=8

implicit derivative

\frac{d y}{d x}, 4 x y = 8

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

Solution steps

4 x y = 8

Treat

y

y (x)

Differentiate both sides:

4 (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}

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\frac{\partial}{\partial x} (x^{y} + y^{x})

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

\int + \frac{4 - 32 x}{1 - 16 x ^{2}} d x

\int \frac{x - 1}{x ( x ^{2} + 1 )} d x

What is implicit (dy)/(dx),4xy=8 ?
The answer to implicit (dy)/(dx),4xy=8 is (dy)/(dx)=-y/x