derivative of (x^2+1^x)

Lösung

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

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

Schritte zur Lösung

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

Wende Exponentenregel an:

a^{b} = e^{b l n (a)}

(x^{2} + 1)^{x} = e^{x l n (x^{2} + 1)}

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

Wende die Kettenregel an:

e^{x l n (x^{2} + 1)} \frac{d}{d x} (x ln (x^{2} + 1))

= e^{x l n (x^{2} + 1)} \frac{d}{d x} (x ln (x^{2} + 1))

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

= e^{x l n (x^{2} + 1)} (ln (x^{2} + 1) + \frac{2 x ^{2}}{x ^{2} + 1})

e^{x l n (x^{2} + 1)} = (x^{2} + 1)^{x}

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

f (x) = ln (1 + e^{x})

a re a ∣ x ∣, x^{2} - 6

y^{^{'}} + 2 y = t, y (0) = 1

\frac{d y}{d x} - 2 y = \frac{2 y}{x}

\int arccot (10 y) d y