derivative of (2x/(sqrt(x^2+2)))

Lösung

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

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

Schritte zur Lösung

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

Entferne die Konstante:

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

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

Wende die Quotientenregel an:

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

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

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

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

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

Vereinfache

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

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

\frac{\partial}{\partial x} (\frac{1}{2})

\frac{d}{d x} (\frac{csc ( x )}{x})

l a pl a ce t r an s f or m t cos (4 t)

y^{^{'}} = (0.5 + sin (t)) (\frac{y}{5})

t a y l or e^{- x}, x = 0