derivative of (x+1^{x^2})

Lösung

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

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

Schritte zur Lösung

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

Wende Exponentenregel an:

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

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

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

Wende die Kettenregel an:

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

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

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

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

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

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

t an g e n t f (x) = x^{2} + a x + 2, at x = 1

\int - 6 ln (x^{2} - 1) d x

\int (x cos (4 x)) d x

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

\frac{d}{d x} (x e^{- x} - e^{- x})