derivative of 4*sqrt(x^2+3x)

Lösung

\frac{d}{d x} (4 \cdot x^{2} + 3 x)

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

Schritte zur Lösung

\frac{d}{d x} (4 x^{2} + 3 x)

Entferne die Konstante:

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

= 4 \frac{d}{d x} (x^{2} + 3 x)

Wende die Kettenregel an:

\frac{1}{2 x ^{2} + 3 x} \frac{d}{d x} (x^{2} + 3 x)

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

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

= 4 \cdot \frac{1}{2 x ^{2} + 3 x} (2 x + 3)

Vereinfache

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

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

\frac{d}{d x} (\frac{4 x}{x - 3})

x y^{2} y^{^{'}} = y^{3} - 3 x^{3}, y (1) = 3

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

\int (x - 5) ln (x) d x

s l o p e y = 3 - 4 x^{2}, (- 1, - 1)