derivative of (3+csc(x)/(7-csc(x)))

Lösung

\frac{d}{d x} (\frac{3 + csc ( x )}{7 - csc ( x )})

- \frac{10 cot ( x ) csc ( x )}{( 7 - csc ( x ) ) ^{2}}

Schritte zur Lösung

\frac{d}{d x} (\frac{3 + csc ( x )}{7 - csc ( x )})

Wende die Quotientenregel an:

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

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

\frac{d}{d x} (3 + csc (x)) = - cot (x) csc (x)

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

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

Vereinfache

\frac{( - cot ( x ) csc ( x ) ) ( 7 - csc ( x ) ) - cot ( x ) csc ( x ) ( 3 + csc ( x ) )}{( 7 - csc ( x ) ) ^{2}} : - \frac{10 cot ( x ) csc ( x )}{( 7 - csc ( x ) ) ^{2}}

= - \frac{10 cot ( x ) csc ( x )}{( 7 - csc ( x ) ) ^{2}}

y^{^{'}} = y + 1 + 2 sin (t)

x \to 0 + lim (\frac{2 x}{ln ( x )})

\int \frac{cos ( x )}{cos ( x )} d x

t an g e n t 8 x^{2} + x y + 8 y^{2} = 17, (1, 1)

d er i v a t i v e y = 4 x^{3} - 12 x + 3