derivative (2x+3)/(3x+2)

Lösung

ableitung von

\frac{2 x + 3}{3 x + 2}

- \frac{5}{( 3 x + 2 ) ^{2}}

Schritte zur Lösung

\frac{d}{d x} (\frac{2 x + 3}{3 x + 2})

Wende die Quotientenregel an:

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

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

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

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

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

Vereinfache

\frac{2 ( 3 x + 2 ) - 3 ( 2 x + 3 )}{( 3 x + 2 ) ^{2}} : - \frac{5}{( 3 x + 2 ) ^{2}}

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

\int_{0}^{1} \frac{z}{( z ^{2} + 1 ) ^{3}} d z

x \to 0 + lim (ln (x^{3}))

(1 + t^{2}) y^{^{'}} + 4 t y = t

x \to - 4 lim (\frac{1}{( x + 4 ) ^{4}})

\frac{d}{d x} (10 x + 4 y)