derivative of ((ax+by(x))/((cx+dy)))

Lösung

\frac{d}{d x} (\frac{( a x + b y ( x ) )}{( c x + d y ( x ) )})

\frac{b c x \frac{d}{d x} ( y ( x ) ) - a d x \frac{d}{d x} ( y ( x ) ) - b c y ( x ) + a d y ( x )}{( c x + d y ( x ) ) ^{2}}

Schritte zur Lösung

\frac{d}{d x} (\frac{( a x + b y ( x ) )}{( c x + d y ( x ) )})

Wende die Quotientenregel an:

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

= \frac{\frac{d}{d x} ( a x + b y ( x ) ) ( c x + d y ( x ) ) - \frac{d}{d x} ( c x + d y ( x ) ) ( a x + b y ( x ) )}{( c x + d y ( x ) ) ^{2}}

\frac{d}{d x} (a x + b y (x)) = a + b \frac{d}{d x} (y (x))

\frac{d}{d x} (c x + d y (x)) = c + d \frac{d}{d x} (y (x))

= \frac{( a + b \frac{d}{d x} ( y ( x ) ) ) ( c x + d y ( x ) ) - ( c + d \frac{d}{d x} ( y ( x ) ) ) ( a x + b y ( x ) )}{( c x + d y ( x ) ) ^{2}}

Multipliziere aus

(a + b \frac{d}{d x} (y (x))) (c x + d y (x)) - (c + d \frac{d}{d x} (y (x))) (a x + b y (x)) : b c x \frac{d}{d x} (y (x)) - a d x \frac{d}{d x} (y (x)) - b c y (x) + a d y (x)

= \frac{b c x \frac{d}{d x} ( y ( x ) ) - a d x \frac{d}{d x} ( y ( x ) ) - b c y ( x ) + a d y ( x )}{( c x + d y ( x ) ) ^{2}}

d er i v a t i v e (x^{2} - 2) (x^{3} - 3 x)

\int \frac{tan ( 3 x )}{cos ( 3 x )} d x

5 y^{^{''}} + y^{^{'}} = - 10 x, y (0) = 0, y^{^{'}} (0) = - 15

t an g e n t f (x) = \frac{2 x + 1}{x + 2}, (1, 1)

\int (x \cdot (1 - x^{4})) d x