derivative f(x)=(e^x)/(8x^2+3)

Lösung

ableitung von

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

\frac{e ^{x} ( 8 x ^{2} + 3 ) - 16 x e ^{x}}{( 8 x ^{2} + 3 ) ^{2}}

Schritte zur Lösung

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

Wende die Quotientenregel an:

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

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

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

\frac{d}{d x} (8 x^{2} + 3) = 16 x

= \frac{e ^{x} ( 8 x ^{2} + 3 ) - 16 x e ^{x}}{( 8 x ^{2} + 3 ) ^{2}}

n = 1 \sum \infty \frac{4 ^{n}}{6 ^{n}}

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

x \to - 1 + lim (ln ∣ x + 1 ∣)

\frac{d}{d x} (x^{2} e^{\frac{- x}{10}})

t an g e n t f (x) = \frac{x}{x ^{2} - 15}, at x = 4