derivative xsqrt(x^2+9)

Lösung

ableitung von

x x^{2} + 9

\frac{2 x ^{2} + 9}{x ^{2} + 9}

Schritte zur Lösung

\frac{d}{d x} (x x^{2} + 9)

Wende die Produktregel an:

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

f = x, g = x^{2} + 9

= \frac{d x}{d x} x^{2} + 9 + \frac{d}{d x} (x^{2} + 9) x

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

\frac{d}{d x} (x^{2} + 9) = \frac{x}{x ^{2} + 9}

= 1 \cdot x^{2} + 9 + \frac{x}{x ^{2} + 9} x

Vereinfache

1 \cdot x^{2} + 9 + \frac{x}{x ^{2} + 9} x : \frac{2 x ^{2} + 9}{x ^{2} + 9}

= \frac{2 x ^{2} + 9}{x ^{2} + 9}

y^{^{''}} + 2 y^{^{'}} + 10 y = 0, y (0) = 3, y^{^{'}} (0) = - 1

\frac{d}{d x} (\frac{e ^{6 x}}{x})

x \to 3 lim (x + 3)

d er i v a t i v e - \frac{18}{x ^{3}}

\frac{d y}{d x} = \frac{x y + y ^{2} + x ^{2}}{x ^{2}}