What is implicit (dy)/(dx),y= 6/x ?

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

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implicit (dy)/(dx),y= 6/x

implicit derivative

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

\frac{d y}{d x} = - \frac{6}{x ^{2}}

Solution steps

y = \frac{6}{x}

Treat

y

y (x)

Differentiate both sides:

\frac{d y}{d x} = - \frac{6}{x ^{2}}

Isolate

\frac{d y}{d x} : \frac{d y}{d x} = - \frac{6}{x ^{2}}

\frac{d y}{d x} = - \frac{6}{x ^{2}}

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

(3.11) (11.8)

\int_{- \frac{π}{2}}^{\frac{π}{2}} sin (x) d x

4 x + y^{2} = 12, y = x

x \to 0 lim (\frac{sin ( 2 x )}{3 x})

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