derivative of e^{y-ln(x})

Lösung

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

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

Schritte zur Lösung

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

Wende die Kettenregel an:

e^{y - l n (x)} \frac{d}{d x} (y - ln (x))

= e^{y - l n (x)} \frac{d}{d x} (y - ln (x))

\frac{d}{d x} (y - ln (x)) = \frac{d y}{d x} - \frac{1}{x}

= e^{y - l n (x)} (\frac{d y}{d x} - \frac{1}{x})

Vereinfache

e^{y - l n (x)} (\frac{d y}{d x} - \frac{1}{x}) : \frac{e ^{y} ( x \frac{d y}{d x} - 1 )}{x ^{2}}

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

\frac{d}{d x} (\frac{x ^{4}}{x ^{5} + 3})

\frac{\partial}{\partial y} (3 x + y)

\int \frac{23}{23 + e ^{x}} d x

\frac{\partial}{\partial x} (x y + ln (x + y))

\frac{d}{d x} (sin^{l n (x)} (3 x))