What is implicit (dy)/(dx),y=((x^2+2x))/(4-5x) ?

The answer to implicit (dy)/(dx),y=((x^2+2x))/(4-5x) is (dy)/(dx)=(-5x^2+8x+8)/((4-5x)^2)

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implicit (dy)/(dx),y=((x^2+2x))/(4-5x)

implicit derivative

\frac{d y}{d x}, y = \frac{( x ^{2} + 2 x )}{4 - 5 x}

\frac{d y}{d x} = \frac{- 5 x ^{2} + 8 x + 8}{( 4 - 5 x ) ^{2}}

Solution steps

y = \frac{x ^{2} + 2 x}{4 - 5 x}

Treat

y

y (x)

Differentiate both sides:

\frac{d y}{d x} = \frac{- 5 x ^{2} + 8 x + 8}{( 4 - 5 x ) ^{2}}

Isolate

\frac{d y}{d x} : \frac{d y}{d x} = \frac{- 5 x ^{2} + 8 x + 8}{( 4 - 5 x ) ^{2}}

\frac{d y}{d x} = \frac{- 5 x ^{2} + 8 x + 8}{( 4 - 5 x ) ^{2}}

What is implicit (dy)/(dx),y=((x^2+2x))/(4-5x) ?
The answer to implicit (dy)/(dx),y=((x^2+2x))/(4-5x) is (dy)/(dx)=(-5x^2+8x+8)/((4-5x)^2)