implicit e^{x^2y}=x+y

Lösung

implizite ableitung

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

\frac{d y}{d x} = \frac{1 - 2 e ^{x^{2} y} x y}{e ^{x^{2} y} x ^{2} - 1}

Schritte zur Lösung

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

Behandle

y

wie

y (x)

Beide Seiten differenzieren:

e^{x^{2} y} (2 x y + \frac{d y}{d x} x^{2}) = 1 + \frac{d y}{d x}

Isoliere

\frac{d y}{d x} : \frac{d y}{d x} = \frac{1 - 2 e ^{x^{2} y} x y}{e ^{x^{2} y} x ^{2} - 1}

\frac{d y}{d x} = \frac{1 - 2 e ^{x^{2} y} x y}{e ^{x^{2} y} x ^{2} - 1}

\frac{d}{d x} (- \frac{8}{1 - 8 x})

d er i v a t i v e (2 - x^{2})^{\frac{1}{2}}

\int_{0}^{1} \frac{1}{x + 1} d x

\int_{0}^{1} (x + x) d x

\int \frac{( 6 - x )}{4 x ^{2} - 12 x + 7} d x