derivative of \sqrt[4]{(e^{5x}/(x^2+1)})

Lösung

\frac{d}{d x} (4 \frac{e ^{5 x}}{x ^{2} + 1})

\frac{e ^{\frac{5 x}{4}} ( 5 ( x ^{2} + 1 ) - 2 x )}{4 ( x ^{2} + 1 ) ^{\frac{5}{4}}}

Schritte zur Lösung

\frac{d}{d x} (4 \frac{e ^{5 x}}{x ^{2} + 1})

Wende die Kettenregel an:

\frac{1}{4 ( \frac{e ^{5 x}}{x ^{2} + 1} ) ^{\frac{3}{4}}} \frac{d}{d x} (\frac{e ^{5 x}}{x ^{2} + 1})

= \frac{1}{4 ( \frac{e ^{5 x}}{x ^{2} + 1} ) ^{\frac{3}{4}}} \frac{d}{d x} (\frac{e ^{5 x}}{x ^{2} + 1})

\frac{d}{d x} (\frac{e ^{5 x}}{x ^{2} + 1}) = \frac{e ^{5 x} \cdot 5 ( x ^{2} + 1 ) - 2 x e ^{5 x}}{( x ^{2} + 1 ) ^{2}}

= \frac{1}{4 ( \frac{e ^{5 x}}{x ^{2} + 1} ) ^{\frac{3}{4}}} \cdot \frac{e ^{5 x} \cdot 5 ( x ^{2} + 1 ) - 2 x e ^{5 x}}{( x ^{2} + 1 ) ^{2}}

Vereinfache

\frac{1}{4 ( \frac{e ^{5 x}}{x ^{2} + 1} ) ^{\frac{3}{4}}} \cdot \frac{e ^{5 x} \cdot 5 ( x ^{2} + 1 ) - 2 x e ^{5 x}}{( x ^{2} + 1 ) ^{2}} : \frac{e ^{\frac{5 x}{4}} ( 5 ( x ^{2} + 1 ) - 2 x )}{4 ( x ^{2} + 1 ) ^{\frac{5}{4}}}

= \frac{e ^{\frac{5 x}{4}} ( 5 ( x ^{2} + 1 ) - 2 x )}{4 ( x ^{2} + 1 ) ^{\frac{5}{4}}}

n \to \infty lim (sin (\frac{nπ}{2}))

\int \frac{9}{x ^{2} x ^{2} + 36} d x

x \to 4 - lim (\frac{∣ x - 4 ∣}{x - 4})

\int x a e^{- a x} d x

\int \frac{9}{x ( ln ( x ) ) ^{2}} d x