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Beliebt Rechnen >

derivative of sqrt(x^2+2x-1)

Lösung

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

Lösung

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

Schritte zur Lösung

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

Wende die Kettenregel an:

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

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

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

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

Vereinfache

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

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

Graph

Beliebte Beispiele

xy^'=y+(xy)^{1/2}

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

\frac{d y}{d x} + y = 10

integral from 1 to 4 of (x)

\int_{1}^{4} (x) d x

(d^3)/(dx^3)(e^xcos(x))

\frac{d ^{3}}{d x ^{3}} (e^{x} cos (x))

integral of 9(ln(x))^2

\int 9 (ln (x))^{2} d x