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

Lösung

implizite ableitung

\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}}

Schritte zur Lösung

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

Behandle

y

wie

y (x)

Beide Seiten differenzieren:

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

Isoliere

\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}}

\frac{d}{d x} (\frac{1}{4 x ^{\frac{3}{4}}})

\frac{\partial}{\partial x} (1.85 + 2.05 x + 0.656 y)

x \to 0 lim (sin (1 x))

n = 1 \sum \infty e^{- n}

\frac{d}{d x} (\frac{1}{x ^{4} \cdot ( 5 - x )})