derivative (3+8x)/(9-2x)

Lösung

ableitung von

\frac{3 + 8 x}{9 - 2 x}

\frac{78}{( 9 - 2 x ) ^{2}}

Schritte zur Lösung

\frac{d}{d x} (\frac{3 + 8 x}{9 - 2 x})

Wende die Quotientenregel an:

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

= \frac{\frac{d}{d x} ( 3 + 8 x ) ( 9 - 2 x ) - \frac{d}{d x} ( 9 - 2 x ) ( 3 + 8 x )}{( 9 - 2 x ) ^{2}}

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

\frac{d}{d x} (9 - 2 x) = - 2

= \frac{8 ( 9 - 2 x ) - ( - 2 ) ( 3 + 8 x )}{( 9 - 2 x ) ^{2}}

Vereinfache

\frac{8 ( 9 - 2 x ) - ( - 2 ) ( 3 + 8 x )}{( 9 - 2 x ) ^{2}} : \frac{78}{( 9 - 2 x ) ^{2}}

= \frac{78}{( 9 - 2 x ) ^{2}}

d er i v a t i v e f (t) = (1 t^{2} + 0 t + 0)^{- 8}

\frac{d}{d x} (4^{9^{x^{2}}})

in v erse l a pl a ce \frac{1}{x} \cdot \frac{10}{x ^{2} + x + 10}

\frac{d}{d x} (sin (x^{2} + y^{2}))

a re a y^{2} = 4 x, x = 1, x = 4