derivative of e^{4y-x^2-y^2}

Lösung

\frac{d}{d x} (e^{4 y - x^{2} - y^{2}})

e^{4 y - x^{2} - y^{2}} (4 \frac{d y}{d x} - 2 x - 2 y \frac{d y}{d x})

Schritte zur Lösung

\frac{d}{d x} (e^{4 y - x^{2} - y^{2}})

Wende die Kettenregel an:

e^{4 y - x^{2} - y^{2}} \frac{d}{d x} (4 y - x^{2} - y^{2})

= e^{4 y - x^{2} - y^{2}} \frac{d}{d x} (4 y - x^{2} - y^{2})

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

= e^{4 y - x^{2} - y^{2}} (4 \frac{d y}{d x} - 2 x - 2 y \frac{d y}{d x})

= e^{4 y - x^{2} - y^{2}} (4 \frac{d y}{d x} - 2 x - 2 y \frac{d y}{d x})