derivative f(x)=sqrt(5x+x^2)

Lösung

ableitung von

f (x) = 5 x + x^{2}

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

Schritte zur Lösung

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

Wende die Kettenregel an:

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

= \frac{1}{2 5 x + x ^{2}} \frac{d}{d x} (5 x + x^{2})

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

= \frac{1}{2 5 x + x ^{2}} (5 + 2 x)

Vereinfache

\frac{1}{2 5 x + x ^{2}} (5 + 2 x) : \frac{5 + 2 x}{2 5 x + x ^{2}}

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

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