derivative of x/(sqrt(x^2+3))

Lösung

\frac{d}{d x} (\frac{x}{x ^{2} + 3})

\frac{3}{( x ^{2} + 3 ) x ^{2} + 3}

Schritte zur Lösung

\frac{d}{d x} (\frac{x}{x ^{2} + 3})

Wende die Quotientenregel an:

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

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

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

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

= \frac{1 \cdot x ^{2} + 3 - \frac{x}{x ^{2} + 3} x}{( x ^{2} + 3 ) ^{2}}

Vereinfache

\frac{1 \cdot x ^{2} + 3 - \frac{x}{x ^{2} + 3} x}{( x ^{2} + 3 ) ^{2}} : \frac{3}{( x ^{2} + 3 ) x ^{2} + 3}

= \frac{3}{( x ^{2} + 3 ) x ^{2} + 3}

\frac{d}{d x} (\frac{cot ( x )}{sin ( x )})

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

x \to - 2 lim (\frac{- 9}{x ^{2}})

x \to \infty lim ((5) 66666)

y^{^{''}} + 6 y^{^{'}} + 25 y = 100, y (0) = 0, y^{^{'}} (0) = 0