derivative of (3x+4/(7x-5))

Lösung

\frac{d}{d x} (\frac{3 x + 4}{7 x - 5})

- \frac{43}{( 7 x - 5 ) ^{2}}

Schritte zur Lösung

\frac{d}{d x} (\frac{3 x + 4}{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 + 4 ) ( 7 x - 5 ) - \frac{d}{d x} ( 7 x - 5 ) ( 3 x + 4 )}{( 7 x - 5 ) ^{2}}

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

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

= \frac{3 ( 7 x - 5 ) - 7 ( 3 x + 4 )}{( 7 x - 5 ) ^{2}}

Vereinfache

\frac{3 ( 7 x - 5 ) - 7 ( 3 x + 4 )}{( 7 x - 5 ) ^{2}} : - \frac{43}{( 7 x - 5 ) ^{2}}

= - \frac{43}{( 7 x - 5 ) ^{2}}

t an g e n t (x^{2} - 24)^{6}

t an g e n t 5 x^{2} + 2 x, at x = 3

\int sin^{3} (4 θ) cos (4 θ) d θ

t an g e n t f (x) = x^{2} + 4

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