derivative of (e^x/(3x^2+2x^4))

Lösung

\frac{d}{d x} (\frac{e ^{x}}{3 x ^{2} + 2 x ^{4}})

\frac{e ^{x} ( 2 x ^{3} - 8 x ^{2} + 3 x - 6 )}{x ^{3} ( 2 x ^{2} + 3 ) ^{2}}

Schritte zur Lösung

\frac{d}{d x} (\frac{e ^{x}}{3 x ^{2} + 2 x ^{4}})

Wende die Quotientenregel an:

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

= \frac{\frac{d}{d x} ( e ^{x} ) ( 3 x ^{2} + 2 x ^{4} ) - \frac{d}{d x} ( 3 x ^{2} + 2 x ^{4} ) e ^{x}}{( 3 x ^{2} + 2 x ^{4} ) ^{2}}

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

\frac{d}{d x} (3 x^{2} + 2 x^{4}) = 6 x + 8 x^{3}

= \frac{e ^{x} ( 3 x ^{2} + 2 x ^{4} ) - ( 6 x + 8 x ^{3} ) e ^{x}}{( 3 x ^{2} + 2 x ^{4} ) ^{2}}

Vereinfache

\frac{e ^{x} ( 3 x ^{2} + 2 x ^{4} ) - ( 6 x + 8 x ^{3} ) e ^{x}}{( 3 x ^{2} + 2 x ^{4} ) ^{2}} : \frac{e ^{x} ( 2 x ^{3} - 8 x ^{2} + 3 x - 6 )}{x ^{3} ( 2 x ^{2} + 3 ) ^{2}}

= \frac{e ^{x} ( 2 x ^{3} - 8 x ^{2} + 3 x - 6 )}{x ^{3} ( 2 x ^{2} + 3 ) ^{2}}

\frac{\partial}{\partial x} (2 x sin (8 x^{2} y))

y^{^{'}} = 0.0012 y (1700 - y)

y^{^{'}} = \frac{( 2 x ^{2} + 3 y ^{2} )}{2 x y}

\frac{\partial}{\partial v} (tan (\frac{u}{v}))

n = 3 \sum \infty \frac{2}{n ( n + 2 )}