derivative xsqrt(x^2+5)

Lösung

ableitung von

x x^{2} + 5

\frac{2 x ^{2} + 5}{x ^{2} + 5}

Schritte zur Lösung

\frac{d}{d x} (x x^{2} + 5)

Wende die Produktregel an:

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

f = x, g = x^{2} + 5

= \frac{d x}{d x} x^{2} + 5 + \frac{d}{d x} (x^{2} + 5) x

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

\frac{d}{d x} (x^{2} + 5) = \frac{x}{x ^{2} + 5}

= 1 \cdot x^{2} + 5 + \frac{x}{x ^{2} + 5} x

Vereinfache

1 \cdot x^{2} + 5 + \frac{x}{x ^{2} + 5} x : \frac{2 x ^{2} + 5}{x ^{2} + 5}

= \frac{2 x ^{2} + 5}{x ^{2} + 5}

n = 2 \sum \infty \frac{1}{n}

\frac{d}{d x} (x^{- \frac{1}{5}})

\int \frac{x}{x ^{4} x ^{4} - x ^{2}} d x

d er i v a t i v e f (x) = (x + 1) (x + 1 - \frac{1}{x + 2})

in v erse l a pl a ce \frac{s - 1}{s ( s + 2.5 )}