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Beliebt Rechnen >

implicit (dy)/(dx),xy+4e^y=4e

Lösung

implizite ableitung

\frac{d y}{d x}, x y + 4 e^{y} = 4 e

Lösung

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

Schritte zur Lösung

x y + 4 e^{y} = 4 e

Behandle

y

wie

y (x)

Beide Seiten differenzieren:

y + x \frac{d y}{d x} + e^{y} \frac{d y}{d x} = 0

Isoliere

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

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

Beliebte Beispiele

integral of x^2(x^3+5)^{10}

\int x^{2} (x^{3} + 5)^{10} d x

y^{''}+2y^'+y=3-e^{-t}

y^{^{''}} + 2 y^{^{'}} + y = 3 - e^{- t}

derivative of sec^2(x+tan^2(x))

\frac{d}{d x} (sec^{2} (x) + tan^{2} (x))

integral of cos^8(x)

\int cos^{8} (x) d x

derivative (x^{-2}+x^{-3})(x^5-2x^2)

d er i v a t i v e (x^{- 2} + x^{- 3}) (x^{5} - 2 x^{2})