derivative of (cot(x)/(1+cot(x)))

Lösung

\frac{d}{d x} (\frac{cot ( x )}{1 + cot ( x )})

- \frac{csc ^{2} ( x )}{( 1 + cot ( x ) ) ^{2}}

Schritte zur Lösung

\frac{d}{d x} (\frac{cot ( x )}{1 + cot ( x )})

Wende die Quotientenregel an:

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

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

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

\frac{d}{d x} (1 + cot (x)) = - csc^{2} (x)

= \frac{( - csc ^{2} ( x ) ) ( 1 + cot ( x ) ) - ( - csc ^{2} ( x ) ) cot ( x )}{( 1 + cot ( x ) ) ^{2}}

Vereinfache

\frac{( - csc ^{2} ( x ) ) ( 1 + cot ( x ) ) - ( - csc ^{2} ( x ) ) cot ( x )}{( 1 + cot ( x ) ) ^{2}} : - \frac{csc ^{2} ( x )}{( 1 + cot ( x ) ) ^{2}}

= - \frac{csc ^{2} ( x )}{( 1 + cot ( x ) ) ^{2}}

im pl i c i t \frac{d y}{d x}, y - 5 x y^{3} + 8 = 5 sin (y^{3} + 2 x^{2})

\frac{\partial}{\partial x} (x (y + 1))

\int_{0}^{2 π} sin^{4} (x) d x

\frac{d}{d x} (sin (9 x) + (sin (9 x))^{2})

d er i v a t i v e f (2 x) = 5 x - 3