derivative of 2xsqrt(x^2+1)

Lösung

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

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

Schritte zur Lösung

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

Entferne die Konstante:

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

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

Wende die Produktregel an:

(f \cdot g)^{'} = f^{'} \cdot g + f \cdot g^{'}

f = x, g = x^{2} + 1

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

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

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

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

Vereinfache

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

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

\int \frac{6 x + 7}{( 9 x ^{2} + 21 x ) ^{3}} d x

\frac{d}{d x} (\frac{x ^{2}}{x ^{3} + 8})

\frac{d}{d x} (103 sin (x) - 10 cos (x))

\int \frac{1}{x ^{2} + 60} d x

x \to \infty lim (4 x e^{(\frac{1}{x})} - 4 x)