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Beliebt Rechnen >

derivative of ln(x+sqrt(2+x^2))

Lösung

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

Lösung

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

Schritte zur Lösung

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

Wende die Kettenregel an:

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

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

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

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

Vereinfache

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

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

Graph

Beliebte Beispiele

xy^2y^'=x^3+y^3

x y^{2} y^{^{'}} = x^{3} + y^{3}

integral from 0 to pi/6 of ln(sec(x))

\int_{0}^{\frac{π}{6}} ln (sec (x)) d x

laplacetransform f(t)=t^3

l a pl a ce t r an s f or m f (t) = t^{3}

derivative (qx+r)/(sx+t)

d er i v a t i v e \frac{q x + r}{s x + t}

derivative of ln(x-sin(x))

\frac{d}{d x} (ln (x) - sin (x))