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}}

\int (x + 4) 6 - x d x

\int \frac{2 x ^{3}}{x ^{2} - 4} d x

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

x \to 0 + lim ((csc (x))^{x})

d er i v a t i v e x^{2} + 6 x + 3