derivative of ((sqrt(x)-6)/(sqrt(x)+6))

Lösung

\frac{d}{d x} (\frac{( x - 6 )}{x + 6})

\frac{6}{x ( x + 6 ) ^{2}}

Schritte zur Lösung

\frac{d}{d x} (\frac{( x - 6 )}{x + 6})

Wende die Quotientenregel an:

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

= \frac{\frac{d}{d x} ( x - 6 ) ( x + 6 ) - \frac{d}{d x} ( x + 6 ) ( x - 6 )}{( x + 6 ) ^{2}}

\frac{d}{d x} (x - 6) = \frac{1}{2 x}

\frac{d}{d x} (x + 6) = \frac{1}{2 x}

= \frac{\frac{1}{2 x} ( x + 6 ) - \frac{1}{2 x} ( x - 6 )}{( x + 6 ) ^{2}}

Vereinfache

\frac{\frac{1}{2 x} ( x + 6 ) - \frac{1}{2 x} ( x - 6 )}{( x + 6 ) ^{2}} : \frac{6}{x ( x + 6 ) ^{2}}

= \frac{6}{x ( x + 6 ) ^{2}}

s im pl i f y (\frac{1 + sin ( t )}{1 - cos ( t )})^{2}

\int_{0}^{\infty} 9 sin^{2} (x) d x

(x - y^{2} x) d x + (y - x^{2} y) d y = 0

a re a x = 6 - y^{2}, x = y

d er i v a t i v e y = x^{3} - 3 x + 2