derivative of (3x+1/(7x+5))

Lösung

\frac{d}{d x} (\frac{3 x + 1}{7 x + 5})

\frac{8}{( 7 x + 5 ) ^{2}}

Schritte zur Lösung

\frac{d}{d x} (\frac{3 x + 1}{7 x + 5})

Wende die Quotientenregel an:

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

= \frac{\frac{d}{d x} ( 3 x + 1 ) ( 7 x + 5 ) - \frac{d}{d x} ( 7 x + 5 ) ( 3 x + 1 )}{( 7 x + 5 ) ^{2}}

\frac{d}{d x} (3 x + 1) = 3

\frac{d}{d x} (7 x + 5) = 7

= \frac{3 ( 7 x + 5 ) - 7 ( 3 x + 1 )}{( 7 x + 5 ) ^{2}}

Multipliziere aus

3 (7 x + 5) - 7 (3 x + 1) : 8

= \frac{8}{( 7 x + 5 ) ^{2}}

\frac{d}{d x} (\frac{x ^{x}}{sin ( x )})

\frac{d y}{d x} = k \cdot y^{2}

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

d er i v a t i v e f (x) = - 12 x^{2} + 400 x - 3800

t an g e n t 3 x - 4 x^{2}