derivative of (8x/(7-cot(x)))

Lösung

\frac{d}{d x} (\frac{8 x}{7 - cot ( x )})

\frac{8 ( 7 - cot ( x ) - x csc ^{2} ( x ) )}{( 7 - cot ( x ) ) ^{2}}

Schritte zur Lösung

\frac{d}{d x} (\frac{8 x}{7 - cot ( x )})

Entferne die Konstante:

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

= 8 \frac{d}{d x} (\frac{x}{7 - cot ( x )})

Wende die Quotientenregel an:

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

= 8 \cdot \frac{\frac{d x}{d x} ( 7 - cot ( x ) ) - \frac{d}{d x} ( 7 - cot ( x ) ) x}{( 7 - cot ( x ) ) ^{2}}

\frac{d x}{d x} = 1

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

= 8 \cdot \frac{1 \cdot ( 7 - cot ( x ) ) - csc ^{2} ( x ) x}{( 7 - cot ( x ) ) ^{2}}

Vereinfache

8 \cdot \frac{1 \cdot ( 7 - cot ( x ) ) - csc ^{2} ( x ) x}{( 7 - cot ( x ) ) ^{2}} : \frac{8 ( 7 - cot ( x ) - x csc ^{2} ( x ) )}{( 7 - cot ( x ) ) ^{2}}

= \frac{8 ( 7 - cot ( x ) - x csc ^{2} ( x ) )}{( 7 - cot ( x ) ) ^{2}}

a re a x ln (x), - x + 1, [1, 3]

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