derivative of 2arctan(sqrt(sin(x)))

Lösung

\frac{d}{d x} (2 arctan (sin (x)))

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

Schritte zur Lösung

\frac{d}{d x} (2 arctan (sin (x)))

Entferne die Konstante:

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

= 2 \frac{d}{d x} (arctan (sin (x)))

Wende die Kettenregel an:

\frac{1}{( sin ( x ) ) ^{2} + 1} \frac{d}{d x} (sin (x))

= \frac{1}{( sin ( x ) ) ^{2} + 1} \frac{d}{d x} (sin (x))

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

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

Vereinfache

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

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

t an g e n t x^{2} + y^{2} = 25, (3, - 4)

\frac{\partial}{\partial x} (3 x sin (y))

\frac{\partial}{\partial y} (7 x^{\frac{y}{z}})

y^{^{'}} + \frac{2 y}{x} = \frac{2}{x}

\int \frac{u}{u + 1} d u