derivative of ((qx+r(q,x,t))/(sx+t))

Lösung

\frac{d}{d x} (\frac{( q x + r ( q , x , t ) )}{s x + t})

\frac{( q + \frac{d}{d x} ( r ( q , x , t ) ) ) ( s x + t ) - s ( q x + r ( q , x , t ) )}{( s x + t ) ^{2}}

Schritte zur Lösung

\frac{d}{d x} (\frac{( q x + r ( q , x , t ) )}{s x + t})

Behandle

s, q, t

als Konstanten

Wende die Quotientenregel an:

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

= \frac{\frac{d}{d x} ( q x + r ( q , x , t ) ) ( s x + t ) - \frac{d}{d x} ( s x + t ) ( q x + r ( q , x , t ) )}{( s x + t ) ^{2}}

\frac{d}{d x} (q x + r (q, x, t)) = q + \frac{d}{d x} (r (q, x, t))

\frac{d}{d x} (s x + t) = s

= \frac{( q + \frac{d}{d x} ( r ( q , x , t ) ) ) ( s x + t ) - s ( q x + r ( q , x , t ) )}{( s x + t ) ^{2}}

\frac{d y}{d x} = \frac{x + y}{2 x}

\frac{\partial}{\partial x} (\frac{( e ^{y} )}{x + y ^{4}})

x \to - 1 lim (x^{2} - 4)

\frac{d}{d x} (\frac{x + 6}{x ^{2} + 6})

\frac{d}{d x} (3 x^{2} - 5 x + 6)