derivative of (4x/(9y))

Lösung

\frac{d}{d x} (\frac{4 x}{9 y})

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

Schritte zur Lösung

\frac{d}{d x} (\frac{4 x}{9 y})

Entferne die Konstante:

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

= \frac{4}{9} \frac{d}{d x} (\frac{x}{y})

Wende die Quotientenregel an:

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

= \frac{4}{9} \cdot \frac{\frac{d x}{d x} y - \frac{d y}{d x} x}{y ^{2}}

\frac{d x}{d x} = 1

= \frac{4}{9} \cdot \frac{1 \cdot y - \frac{d y}{d x} x}{y ^{2}}

Vereinfache

\frac{4}{9} \cdot \frac{1 \cdot y - \frac{d y}{d x} x}{y ^{2}} : \frac{4 ( y - x \frac{d y}{d x} )}{9 y ^{2}}

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

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

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

x \to 5 lim (\frac{x + 1}{x - 5})

s l o p e (x^{2} - 8)^{4}, at x = 3

t an g e n t f (x) = 7 + 4 x^{2} - 2 x^{3}, at x = 1