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Beliebt Rechnen >

(\partial)/(\partial x)((e^x)/(y+x^7))

Lösung

\frac{\partial}{\partial x} (\frac{e ^{x}}{y + x ^{7}})

Lösung

\frac{e ^{x} ( y + x ^{7} ) - 7 x ^{6} e ^{x}}{( y + x ^{7} ) ^{2}}

Schritte zur Lösung

\frac{\partial}{\partial x} (\frac{e ^{x}}{y + x ^{7}})

Behandle

y

als Konstante

Wende die Quotientenregel an:

(\frac{f}{g})^{'} = \frac{f ^{'} \cdot g - g ^{'} \cdot f}{g ^{2}}

= \frac{\frac{\partial}{\partial x} ( e ^{x} ) ( y + x ^{7} ) - \frac{\partial}{\partial x} ( y + x ^{7} ) e ^{x}}{( y + x ^{7} ) ^{2}}

\frac{\partial}{\partial x} (e^{x}) = e^{x}

\frac{\partial}{\partial x} (y + x^{7}) = 7 x^{6}

= \frac{e ^{x} ( y + x ^{7} ) - 7 x ^{6} e ^{x}}{( y + x ^{7} ) ^{2}}

Beliebte Beispiele

tangent 4x^3-18x^2-48x

t an g e n t 4 x^{3} - 18 x^{2} - 48 x

derivative of 4-2x

\frac{d}{d x} (4 - 2 x)

derivative of arcsec(x+2)

\frac{d}{d x} (arcsec (x + 2))

limit as x approaches infinity of 1/(-x)

x \to \infty lim (\frac{1}{- x})

integral of (2x^3-2/3 x^2+5x)

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