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Beliebt Rechnen >

derivative of (e^{6x}/(x^2+5))

Lösung

\frac{d}{d x} (\frac{e ^{6 x}}{x ^{2} + 5})

Lösung

\frac{e ^{6 x} \cdot 6 ( x ^{2} + 5 ) - 2 x e ^{6 x}}{( x ^{2} + 5 ) ^{2}}

Schritte zur Lösung

\frac{d}{d x} (\frac{e ^{6 x}}{x ^{2} + 5})

Wende die Quotientenregel an:

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

= \frac{\frac{d}{d x} ( e ^{6 x} ) ( x ^{2} + 5 ) - \frac{d}{d x} ( x ^{2} + 5 ) e ^{6 x}}{( x ^{2} + 5 ) ^{2}}

\frac{d}{d x} (e^{6 x}) = e^{6 x} \cdot 6

\frac{d}{d x} (x^{2} + 5) = 2 x

= \frac{e ^{6 x} \cdot 6 ( x ^{2} + 5 ) - 2 x e ^{6 x}}{( x ^{2} + 5 ) ^{2}}

Graph

Beliebte Beispiele

derivative f(t)=(2t-1)^7+14t(2t-1)^6

d er i v a t i v e f (t) = (2 t - 1)^{7} + 14 t (2 t - 1)^{6}

y^'=(x+y-4)^2,y(0)=0

y^{^{'}} = (x + y - 4)^{2}, y (0) = 0

inverselaplace (10)/((2s+3))

in v erse l a pl a ce \frac{10}{( 2 s + 3 )}

vereinfachen (x^4)/4+1/(8x^2)

s im pl i f y \frac{x ^{4}}{4} + \frac{1}{8 x ^{2}}

derivative of (x^2-x+1^{-7})

\frac{d}{d x} ((x^{2} - x + 1)^{- 7})