What is implicit (dy)/(dx),sqrt(xy)=x-2y ?

The answer to implicit (dy)/(dx),sqrt(xy)=x-2y is (dy)/(dx)=((2sqrt(xy)-y)(x-4sqrt(xy)))/(x^2-16xy)

English

Español

Português

Français

Deutsch

Italiano

Русский

中文(简体)

한국어

日本語

Tiếng Việt

עברית

العربية

Popular >

implicit (dy)/(dx),sqrt(xy)=x-2y

implicit derivative

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

\frac{d y}{d x} = \frac{( 2 x y - y ) ( x - 4 x y )}{x ^{2} - 16 x y}

Solution steps

x y = x - 2 y

Treat

y

y (x)

Differentiate both sides:

\frac{y + x \frac{d y}{d x}}{2 x y} = 1 - 2 \frac{d y}{d x}

Isolate

\frac{d y}{d x} : \frac{d y}{d x} = \frac{( 2 x y - y ) ( x - 4 x y )}{x ^{2} - 16 x y}

\frac{d y}{d x} = \frac{( 2 x y - y ) ( x - 4 x y )}{x ^{2} - 16 x y}

\frac{d y}{d x} = \frac{( x - 3 )}{y - 4}

\int \frac{289}{x ^{3} - 17 x ^{2}} d x

\int (1 - t) d t

x \to 0 + lim (I n x)

\int - \frac{1}{x - 1} d x

What is implicit (dy)/(dx),sqrt(xy)=x-2y ?
The answer to implicit (dy)/(dx),sqrt(xy)=x-2y is (dy)/(dx)=((2sqrt(xy)-y)(x-4sqrt(xy)))/(x^2-16xy)