derivative (4x)/(sqrt(x^2+6))

Lösung

ableitung von

\frac{4 x}{x ^{2} + 6}

\frac{24}{( x ^{2} + 6 ) x ^{2} + 6}

Schritte zur Lösung

\frac{d}{d x} (\frac{4 x}{x ^{2} + 6})

Entferne die Konstante:

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

= 4 \frac{d}{d x} (\frac{x}{x ^{2} + 6})

Wende die Quotientenregel an:

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

= 4 \cdot \frac{\frac{d x}{d x} x ^{2} + 6 - \frac{d}{d x} ( x ^{2} + 6 ) x}{( x ^{2} + 6 ) ^{2}}

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

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

= 4 \cdot \frac{1 \cdot x ^{2} + 6 - \frac{x}{x ^{2} + 6} x}{( x ^{2} + 6 ) ^{2}}

Vereinfache

4 \cdot \frac{1 \cdot x ^{2} + 6 - \frac{x}{x ^{2} + 6} x}{( x ^{2} + 6 ) ^{2}} : \frac{24}{( x ^{2} + 6 ) x ^{2} + 6}

= \frac{24}{( x ^{2} + 6 ) x ^{2} + 6}

\int 9 sin^{2} (x) cos^{3} (x) d x

x \to 1 - lim (x ln (x))

t a y l or \frac{5}{x}, 1

\int (tan (2 x) + cot (2 x))^{2} d x

t an g e n t \frac{6 x}{( 3 - 2 x ) ^{3}}