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

Lösung

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

\frac{9}{( x ^{2} + 3 ) x ^{2} + 3}

Schritte zur Lösung

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

Entferne die Konstante:

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

= 3 \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}}

= 3 \cdot \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}

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

Vereinfache

3 \cdot \frac{1 \cdot x ^{2} + 3 - \frac{x}{x ^{2} + 3} x}{( x ^{2} + 3 ) ^{2}} : \frac{9}{( x ^{2} + 3 ) x ^{2} + 3}

= \frac{9}{( x ^{2} + 3 ) x ^{2} + 3}

\frac{d}{d x} (6 arcsin (x^{4}))

\frac{d y}{d x} = x + 5 y, y (0) = 3

x \to 0 lim (cos^{\frac{3}{x ^{2}}} (2 x))

\frac{d y}{d x} = y^{2}

d er i v a t i v e f (x) = \frac{6}{3 x + 1}, at a = - 1