derivative of (5sin(x)/(1+cos(x)))

Lösung

\frac{d}{d x} (\frac{5 sin ( x )}{1 + cos ( x )})

\frac{5}{1 + cos ( x )}

Schritte zur Lösung

\frac{d}{d x} (\frac{5 sin ( x )}{1 + cos ( x )})

Entferne die Konstante:

(a \cdot f)^{'} = a \cdot f^{'}

= 5 \frac{d}{d x} (\frac{sin ( x )}{1 + cos ( x )})

Wende die Quotientenregel an:

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

= 5 \cdot \frac{\frac{d}{d x} ( sin ( x ) ) ( 1 + cos ( x ) ) - \frac{d}{d x} ( 1 + cos ( x ) ) sin ( x )}{( 1 + cos ( x ) ) ^{2}}

\frac{d}{d x} (sin (x)) = cos (x)

\frac{d}{d x} (1 + cos (x)) = - sin (x)

= 5 \cdot \frac{cos ( x ) ( 1 + cos ( x ) ) - ( - sin ( x ) ) sin ( x )}{( 1 + cos ( x ) ) ^{2}}

Vereinfache

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

= \frac{5}{1 + cos ( x )}

\int_{0}^{3} (∣ 2 x - 3 ∣) d x

a re a ∣ x - 15 ∣, \frac{x}{2}

y^{^{''}} + 36 = 0

y^{^{'}} + \frac{y}{x} = 6 x

t an g e n t f (x) = x^{2} + x, (- 4, 12)