derivative of (3x-4/(12x^2))

Lösung

\frac{d}{d x} (\frac{3 x - 4}{12 x ^{2}})

\frac{- 3 x + 8}{12 x ^{3}}

Schritte zur Lösung

\frac{d}{d x} (\frac{3 x - 4}{12 x ^{2}})

Entferne die Konstante:

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

= \frac{1}{12} \frac{d}{d x} (\frac{3 x - 4}{x ^{2}})

Wende die Quotientenregel an:

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

= \frac{1}{12} \cdot \frac{\frac{d}{d x} ( 3 x - 4 ) x ^{2} - \frac{d}{d x} ( x ^{2} ) ( 3 x - 4 )}{( x ^{2} ) ^{2}}

\frac{d}{d x} (3 x - 4) = 3

\frac{d}{d x} (x^{2}) = 2 x

= \frac{1}{12} \cdot \frac{3 x ^{2} - 2 x ( 3 x - 4 )}{( x ^{2} ) ^{2}}

Vereinfache

\frac{1}{12} \cdot \frac{3 x ^{2} - 2 x ( 3 x - 4 )}{( x ^{2} ) ^{2}} : \frac{- 3 x + 8}{12 x ^{3}}

= \frac{- 3 x + 8}{12 x ^{3}}

s l o p e F (x) = x + 1

y^{^{'}} = \frac{( x ^{2} - y ^{2} )}{x y}, y (2) = 2

d er i v a t i v e cos^{4} (x)

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

a re a 2 x^{2} - 1, 0, 1