derivative of 2sqrt(\sqrt{1+x^2)+1}

Lösung

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

\frac{x}{1 + x ^{2} + 1 x ^{2} + 1}

Schritte zur Lösung

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

Entferne die Konstante:

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

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

Wende die Kettenregel an:

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

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

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

= 2 \cdot \frac{1}{2 1 + x ^{2} + 1} \cdot \frac{x}{x ^{2} + 1}

Vereinfache

2 \cdot \frac{1}{2 1 + x ^{2} + 1} \cdot \frac{x}{x ^{2} + 1} : \frac{x}{1 + x ^{2} + 1 x ^{2} + 1}

= \frac{x}{1 + x ^{2} + 1 x ^{2} + 1}

x \to 3 lim (ln (x^{2} - 9))

\int \frac{5 x ^{2} + 20 x + 6}{x ( x + 1 ) ^{2}} d x

\int x (2 x - 3) d x

\frac{\partial}{\partial x} (x^{3} - 6 x y + y^{3} - 2)

\frac{d}{d t} (+ 6 t)