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Beliebt Rechnen >

derivative of ln(x+sqrt(9+x^2))

Lösung

\frac{d}{d x} (ln (x + 9 + x^{2}))

Lösung

\frac{1}{9 + x ^{2}}

Schritte zur Lösung

\frac{d}{d x} (ln (x + 9 + x^{2}))

Wende die Kettenregel an:

\frac{1}{x + 9 + x ^{2}} \frac{d}{d x} (x + 9 + x^{2})

= \frac{1}{x + 9 + x ^{2}} \frac{d}{d x} (x + 9 + x^{2})

\frac{d}{d x} (x + 9 + x^{2}) = 1 + \frac{x}{9 + x ^{2}}

= \frac{1}{x + 9 + x ^{2}} (1 + \frac{x}{9 + x ^{2}})

Vereinfache

\frac{1}{x + 9 + x ^{2}} (1 + \frac{x}{9 + x ^{2}}) : \frac{1}{9 + x ^{2}}

= \frac{1}{9 + x ^{2}}

Graph

Beliebte Beispiele

fläche 2x+1,x^2-4x

a re a 2 x + 1, x^{2} - 4 x

(d^2)/(dx^2)((e^x)/(5+e^x))

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

f(x)=(x^3-2x^2+3x+1)^{11}

f (x) = (x^{3} - 2 x^{2} + 3 x + 1)^{11}

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

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

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y^{^{''}} + 4 y^{^{'}} + 8 y = 0