What is implicit cos(yx^3)= 1/6 ?

The answer to implicit cos(yx^3)= 1/6 is (dy}{dx}=-\frac{3y)/x

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implicit cos(yx^3)= 1/6

implicit derivative

cos (y x^{3}) = \frac{1}{6}

\frac{d y}{d x} = - \frac{3 y}{x}

Solution steps

cos (y x^{3}) = \frac{1}{6}

Treat

y

y (x)

Differentiate both sides:

- sin (y x^{3}) (\frac{d y}{d x} x^{3} + 3 x^{2} y) = 0

Isolate

\frac{d y}{d x} : \frac{d y}{d x} = - \frac{3 y}{x}

\frac{d y}{d x} = - \frac{3 y}{x}

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

y = \frac{x ^{2}}{x}

\int \frac{1}{x} - \frac{2}{x ^{2}} + \frac{5}{x ^{3}} d x

\frac{d}{d t} (z (t))

f (x) = x^{2} e^{x} - 2 x e^{x} + 4 e^{x}

What is implicit cos(yx^3)= 1/6 ?
The answer to implicit cos(yx^3)= 1/6 is (dy}{dx}=-\frac{3y)/x