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

Lösung

\frac{d}{d x} (4 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 x}{d t} = \frac{x}{t}

\frac{\partial}{\partial x} (\frac{1}{∣ x - a ∣})

a re a x = y^{2} - 6 y, x = 5 y - y^{2}

\int \frac{- 1}{y ^{2}} d y

\int 3 x + 4 d x