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Beliebt Rechnen >

implicit (dy)/(dx),sqrt(x+y)+xy=21

Lösung

implizite ableitung

\frac{d y}{d x}, x + y + x y = 21

Lösung

\frac{d y}{d x} = \frac{( - 2 y x + y - 1 ) ( 1 - 2 x x + y )}{1 - 4 x ^{3} - 4 x ^{2} y}

Schritte zur Lösung

x + y + x y = 21

Behandle

y

wie

y (x)

Beide Seiten differenzieren:

\frac{1 + \frac{d y}{d x}}{2 x + y} + y + x \frac{d y}{d x} = 0

Isoliere

\frac{d y}{d x} : \frac{d y}{d x} = \frac{( - 2 y x + y - 1 ) ( 1 - 2 x x + y )}{1 - 4 x ^{3} - 4 x ^{2} y}

\frac{d y}{d x} = \frac{( - 2 y x + y - 1 ) ( 1 - 2 x x + y )}{1 - 4 x ^{3} - 4 x ^{2} y}

Beliebte Beispiele

derivative of x^2cos(xy)

\frac{d}{d x} (x^{2} cos (x y))

derivative of cos(7pix)

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\int sin^{\frac{1}{2}} (x) cos^{3} (x) d x

limit as n approaches infinity of \sum_{i=1}^n(i^3)/(n^4)+1/n

n \to \infty lim (i = 1 \sum n \frac{i ^{3}}{n ^{4}} + \frac{1}{n})

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\frac{d}{d x} (x cos (y) - y e^{x})