d/(da)((pi(9a^2+6a+1))/(54a))

Lösung

\frac{d}{d a} (\frac{π ( 9 a ^{2} + 6 a + 1 )}{54 a})

\frac{π ( 9 a ^{2} - 1 )}{54 a ^{2}}

Schritte zur Lösung

\frac{d}{d a} (\frac{π ( 9 a ^{2} + 6 a + 1 )}{54 a})

Entferne die Konstante:

(a \cdot f)^{'} = a \cdot f^{'}

= \frac{π}{54} \frac{d}{d a} (\frac{9 a ^{2} + 6 a + 1}{a})

Wende die Quotientenregel an:

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

= \frac{π}{54} \cdot \frac{\frac{d}{d a} ( 9 a ^{2} + 6 a + 1 ) a - \frac{d a}{d a} ( 9 a ^{2} + 6 a + 1 )}{a ^{2}}

\frac{d}{d a} (9 a^{2} + 6 a + 1) = 18 a + 6

\frac{d a}{d a} = 1

= \frac{π}{54} \cdot \frac{( 18 a + 6 ) a - 1 \cdot ( 9 a ^{2} + 6 a + 1 )}{a ^{2}}

Vereinfache

\frac{π}{54} \cdot \frac{( 18 a + 6 ) a - 1 \cdot ( 9 a ^{2} + 6 a + 1 )}{a ^{2}} : \frac{π ( 9 a ^{2} - 1 )}{54 a ^{2}}

= \frac{π ( 9 a ^{2} - 1 )}{54 a ^{2}}

\int \frac{e ^{x}}{e ^{2 x} - 2} d x

x \to π lim ((π - x) csc (x))

9 x y^{2} - 3 + (9 x^{2} y + 4) \frac{d y}{d x} = 0

\frac{d y}{d x} + 4 y = 6

\int (x - 2)^{- 3} d x