derivative (x^3+sin(x))/(7x-cot(x))

Lösung

ableitung von

\frac{x ^{3} + sin ( x )}{7 x - cot ( x )}

\frac{14 x ^{3} - x ^{3} csc ^{2} ( x ) - 3 x ^{2} cot ( x ) + 7 x cos ( x ) - cos ( x ) cot ( x ) - 7 sin ( x ) - csc ( x )}{( 7 x - cot ( x ) ) ^{2}}

Schritte zur Lösung

\frac{d}{d x} (\frac{x ^{3} + sin ( x )}{7 x - cot ( x )})

Wende die Quotientenregel an:

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

= \frac{\frac{d}{d x} ( x ^{3} + sin ( x ) ) ( 7 x - cot ( x ) ) - \frac{d}{d x} ( 7 x - cot ( x ) ) ( x ^{3} + sin ( x ) )}{( 7 x - cot ( x ) ) ^{2}}

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

\frac{d}{d x} (7 x - cot (x)) = 7 + csc^{2} (x)

= \frac{( 3 x ^{2} + cos ( x ) ) ( 7 x - cot ( x ) ) - ( 7 + csc ^{2} ( x ) ) ( x ^{3} + sin ( x ) )}{( 7 x - cot ( x ) ) ^{2}}

Vereinfache

\frac{( 3 x ^{2} + cos ( x ) ) ( 7 x - cot ( x ) ) - ( 7 + csc ^{2} ( x ) ) ( x ^{3} + sin ( x ) )}{( 7 x - cot ( x ) ) ^{2}} : \frac{14 x ^{3} - x ^{3} csc ^{2} ( x ) - 3 x ^{2} cot ( x ) + 7 x cos ( x ) - cos ( x ) cot ( x ) - 7 sin ( x ) - csc ( x )}{( 7 x - cot ( x ) ) ^{2}}

= \frac{14 x ^{3} - x ^{3} csc ^{2} ( x ) - 3 x ^{2} cot ( x ) + 7 x cos ( x ) - cos ( x ) cot ( x ) - 7 sin ( x ) - csc ( x )}{( 7 x - cot ( x ) ) ^{2}}

\int 2 (e^{2 t} + 2) d t

y^{^{'}} + \frac{1}{3} y = e^{x} y^{4}

\frac{\partial}{\partial x} (7 cos (y e^{x y}) sin (x))

l a pl a ce t r an s f or m sin (t) \cdot sin (3 t)

\int x sin^{2} (4 x) d x