derivative of ({f}(x)/({g)(x)-2})

Lösung

\frac{d}{d x} (\frac{f ( x )}{g ( x ) - 2})

\frac{\frac{d}{d x} ( f ( x ) ) ( g ( x ) - 2 ) - \frac{d}{d x} ( g ( x ) ) f ( x )}{( g ( x ) - 2 ) ^{2}}

Schritte zur Lösung

\frac{d}{d x} (\frac{f ( x )}{g ( x ) - 2})

Wende die Quotientenregel an:

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

= \frac{\frac{d}{d x} ( f ( x ) ) ( g ( x ) - 2 ) - \frac{d}{d x} ( g ( x ) - 2 ) f ( x )}{( g ( x ) - 2 ) ^{2}}

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

= \frac{\frac{d}{d x} ( f ( x ) ) ( g ( x ) - 2 ) - \frac{d}{d x} ( g ( x ) ) f ( x )}{( g ( x ) - 2 ) ^{2}}

im pl i c i t \frac{d y}{d x}, 3 x y + 1 = 0

\int_{0}^{33} 3 (x - 1)^{- \frac{1}{5}} d x

x y \frac{d y}{d x} = 2 y^{2} - x^{2}

\int 5 x^{\frac{1}{2}} d x

\frac{\partial}{\partial y} (\frac{x ^{2} - y ^{2}}{x y})