derivative of (3sin(x-11cos(x))/(x-2))

Lösung

\frac{d}{d x} (\frac{3 sin ( x ) - 11 cos ( x )}{x - 2})

\frac{3 x cos ( x ) + 11 x sin ( x ) + 5 cos ( x ) - 25 sin ( x )}{( x - 2 ) ^{2}}

Schritte zur Lösung

\frac{d}{d x} (\frac{3 sin ( x ) - 11 cos ( x )}{x - 2})

Wende die Quotientenregel an:

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

= \frac{\frac{d}{d x} ( 3 sin ( x ) - 11 cos ( x ) ) ( x - 2 ) - \frac{d}{d x} ( x - 2 ) ( 3 sin ( x ) - 11 cos ( x ) )}{( x - 2 ) ^{2}}

\frac{d}{d x} (3 sin (x) - 11 cos (x)) = 3 cos (x) + 11 sin (x)

\frac{d}{d x} (x - 2) = 1

= \frac{( 3 cos ( x ) + 11 sin ( x ) ) ( x - 2 ) - 1 \cdot ( 3 sin ( x ) - 11 cos ( x ) )}{( x - 2 ) ^{2}}

Vereinfache

\frac{( 3 cos ( x ) + 11 sin ( x ) ) ( x - 2 ) - 1 \cdot ( 3 sin ( x ) - 11 cos ( x ) )}{( x - 2 ) ^{2}} : \frac{3 x cos ( x ) + 11 x sin ( x ) + 5 cos ( x ) - 25 sin ( x )}{( x - 2 ) ^{2}}

= \frac{3 x cos ( x ) + 11 x sin ( x ) + 5 cos ( x ) - 25 sin ( x )}{( x - 2 ) ^{2}}

n = 1 \sum \infty \frac{n ^{n}}{5 ^{n}}

\int \frac{1}{3 - 6 x} d x

\frac{d}{d x} (x^{2} sin (x) tan (x))

y^{^{''}} + 4 y^{^{'}} - 5 = 0

h \to 0 lim (\frac{h}{h ^{2} + 7 h + 1})