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Beliebt Rechnen >

derivative f(x)=sqrt(x^2+x+1)

Lösung

ableitung von

f (x) = x^{2} + x + 1

Lösung

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

Schritte zur Lösung

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

Wende die Kettenregel an:

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

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

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

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

Vereinfache

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

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

Graph

Beliebte Beispiele

integral of 1/(p-p^2)

\int \frac{1}{p - p ^{2}} d p

derivative of arccsc(-x^2)

\frac{d}{d x} (arccsc (- x^{2}))

integral of (tan^2(x))/(2sec(x))

\int \frac{tan ^{2} ( x )}{2 sec ( x )} d x

integral from 0 to pi of 4xcos(x)

\int_{0}^{π} 4 x cos (x) d x

derivative of 1/(in(x-1))

\frac{d}{d x} (\frac{1}{in ( x - 1 )})