derivative of xcos(y-ye^x)

Lösung

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

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

Schritte zur Lösung

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

Wende die Summen-/Differenzregel an:

(f \pm g)^{'} = f^{'} \pm g^{'}

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

\frac{d}{d x} (x cos (y)) = cos (y) - x sin (y) \frac{d y}{d x}

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

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

Vereinfache

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

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

x \to 5 lim (\frac{x ^{2} - 7 x + 10}{x ^{2} - 25})

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

\int \frac{sec ^{6} ( x )}{tan ^{3} ( x )} d x

x \to 0 - lim (e^{\frac{3}{x}})

x \to 0 lim (\frac{x + 5}{3 x})