derivative f(x)=4sqrt(6x^2+7)

Lösung

ableitung von

f (x) = 4 6 x^{2} + 7

\frac{24 x}{6 x ^{2} + 7}

Schritte zur Lösung

\frac{d}{d x} (4 6 x^{2} + 7)

Entferne die Konstante:

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

= 4 \frac{d}{d x} (6 x^{2} + 7)

Wende die Kettenregel an:

\frac{1}{2 6 x ^{2} + 7} \frac{d}{d x} (6 x^{2} + 7)

= \frac{1}{2 6 x ^{2} + 7} \frac{d}{d x} (6 x^{2} + 7)

\frac{d}{d x} (6 x^{2} + 7) = 12 x

= 4 \cdot \frac{1}{2 6 x ^{2} + 7} \cdot 12 x

Vereinfache

4 \cdot \frac{1}{2 6 x ^{2} + 7} \cdot 12 x : \frac{24 x}{6 x ^{2} + 7}

= \frac{24 x}{6 x ^{2} + 7}

\frac{\partial}{\partial x} (sin (x) + sin (y))

\int 4 x + x d x

s l o p e 5 x^{3} + 10 x^{2} - 2 x + 1

d er i v a t i v e x^{2} - 2 x + 1

2 x y + 6 x + (x^{2} - 4) y^{^{'}} = 0