derivative of (e^{2x}/(x-3))

Lösung

\frac{d}{d x} (\frac{e ^{2 x}}{x - 3})

\frac{2 e ^{2 x} x - 7 e ^{2 x}}{( x - 3 ) ^{2}}

Schritte zur Lösung

\frac{d}{d x} (\frac{e ^{2 x}}{x - 3})

Wende die Quotientenregel an:

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

= \frac{\frac{d}{d x} ( e ^{2 x} ) ( x - 3 ) - \frac{d}{d x} ( x - 3 ) e ^{2 x}}{( x - 3 ) ^{2}}

\frac{d}{d x} (e^{2 x}) = e^{2 x} \cdot 2

\frac{d}{d x} (x - 3) = 1

= \frac{e ^{2 x} \cdot 2 ( x - 3 ) - 1 \cdot e ^{2 x}}{( x - 3 ) ^{2}}

Vereinfache

\frac{e ^{2 x} \cdot 2 ( x - 3 ) - 1 \cdot e ^{2 x}}{( x - 3 ) ^{2}} : \frac{2 e ^{2 x} x - 7 e ^{2 x}}{( x - 3 ) ^{2}}

= \frac{2 e ^{2 x} x - 7 e ^{2 x}}{( x - 3 ) ^{2}}

\frac{d y}{d t} = e^{- 3 t}, y (0) = 10

d er i v a t i v e (x - 1)^{2} (2 x + 1)^{4}

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

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

\int \frac{2 - 2 x}{1 - x} d x