derivative (2x^3+5)/(4x^2+7)

Lösung

ableitung von

\frac{2 x ^{3} + 5}{4 x ^{2} + 7}

\frac{8 x ^{4} + 42 x ^{2} - 40 x}{( 4 x ^{2} + 7 ) ^{2}}

Schritte zur Lösung

\frac{d}{d x} (\frac{2 x ^{3} + 5}{4 x ^{2} + 7})

Wende die Quotientenregel an:

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

= \frac{\frac{d}{d x} ( 2 x ^{3} + 5 ) ( 4 x ^{2} + 7 ) - \frac{d}{d x} ( 4 x ^{2} + 7 ) ( 2 x ^{3} + 5 )}{( 4 x ^{2} + 7 ) ^{2}}

\frac{d}{d x} (2 x^{3} + 5) = 6 x^{2}

\frac{d}{d x} (4 x^{2} + 7) = 8 x

= \frac{6 x ^{2} ( 4 x ^{2} + 7 ) - 8 x ( 2 x ^{3} + 5 )}{( 4 x ^{2} + 7 ) ^{2}}

Multipliziere aus

6 x^{2} (4 x^{2} + 7) - 8 x (2 x^{3} + 5) : 8 x^{4} + 42 x^{2} - 40 x

= \frac{8 x ^{4} + 42 x ^{2} - 40 x}{( 4 x ^{2} + 7 ) ^{2}}

t a y l or 1 + x^{2}

d er i v a t i v e - \frac{1}{4} (x^{- 4} - x^{8})

l a pl a ce t r an s f or m e^{- \frac{π}{2} t}

\int e^{\frac{1}{2} x^{2}} \cdot x^{3} d x

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