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Beliebt Rechnen >

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

Lösung

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

Lösung

I n (1 + \frac{x}{x ^{2} + 1})

Schritte zur Lösung

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

Behandle

n, I

als Konstante

Entferne die Konstante:

(a \cdot f)^{'} = a \cdot f^{'}

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

Wende die Summen-/Differenzregel an:

(f \pm g)^{'} = f^{'} \pm g^{'}

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

\frac{d x}{d x} = 1

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

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

Graph

Beliebte Beispiele

derivative 3x^2-7x^3+x^4-5-3x

d er i v a t i v e 3 x^{2} - 7 x^{3} + x^{4} - 5 - 3 x

y^'=((t^2+3y^2))/(2ty)

y^{^{'}} = \frac{( t ^{2} + 3 y ^{2} )}{2 t y}

sum from n=0 to infinity of (-7/10)^n

n = 0 \sum \infty (- \frac{7}{10})^{n}

fläche 2y=4x-x^2,2y=x-4

a re a 2 y = 4 x - x^{2}, 2 y = x - 4

derivative f(x)=x^2+4x-3

d er i v a t i v e f (x) = x^{2} + 4 x - 3