derivative of (sqrt(x)-4/(sqrt(x)+4))

Lösung

\frac{d}{d x} (\frac{x - 4}{x + 4})

\frac{4}{x ( x + 4 ) ^{2}}

Schritte zur Lösung

\frac{d}{d x} (\frac{x - 4}{x + 4})

Wende die Quotientenregel an:

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

= \frac{\frac{d}{d x} ( x - 4 ) ( x + 4 ) - \frac{d}{d x} ( x + 4 ) ( x - 4 )}{( x + 4 ) ^{2}}

\frac{d}{d x} (x - 4) = \frac{1}{2 x}

\frac{d}{d x} (x + 4) = \frac{1}{2 x}

= \frac{\frac{1}{2 x} ( x + 4 ) - \frac{1}{2 x} ( x - 4 )}{( x + 4 ) ^{2}}

Vereinfache

\frac{\frac{1}{2 x} ( x + 4 ) - \frac{1}{2 x} ( x - 4 )}{( x + 4 ) ^{2}} : \frac{4}{x ( x + 4 ) ^{2}}

= \frac{4}{x ( x + 4 ) ^{2}}

t an g e n t f (x) = \frac{1 - x}{1 + x}, (2, - \frac{1}{3})

n = 1 \sum \infty \frac{n}{ln ( n + 1 )}

\int 2 x^{17} e^{- x^{9}} d x

y^{^{'''}} - 5 y^{^{''}} + 6 y^{^{'}} = 2 sin (x) + 8

d er i v a t i v e y = x^{6 c o s (x)}