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Beliebt Rechnen >

implicit (dy)/(dx),e^{xy}+x^2-y^2=12

Lösung

implizite ableitung

\frac{d y}{d x}, e^{x y} + x^{2} - y^{2} = 12

Lösung

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

Schritte zur Lösung

e^{x y} + x^{2} - y^{2} = 12

Behandle

y

wie

y (x)

Beide Seiten differenzieren:

e^{x y} (y + x \frac{d y}{d x}) + 2 x - 2 y \frac{d y}{d x} = 0

Isoliere

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

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

Beliebte Beispiele

sum from n=0 to infinity of (1/17)^n

n = 0 \sum \infty (\frac{1}{17})^{n}

limit as x approaches 0 of (sin(5x))/(6x)

x \to 0 lim (\frac{sin ( 5 x )}{6 x})

derivative f(x)=3sec(5x)

d er i v a t i v e f (x) = 3 sec (5 x)

derivative (1-6t)/(5+t)

d er i v a t i v e \frac{1 - 6 t}{5 + t}

integral of 11tan^4(xse)c^6x

\int 11 tan^{4} (x se) c^{6} x d x