derivative x^{2x+1}

Lösung

ableitung von

x^{2 x + 1}

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

Schritte zur Lösung

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

Wende Exponentenregel an:

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

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

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

Wende die Kettenregel an:

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

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

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

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

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

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

x \to 5 lim (\frac{1}{x - 5})

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

t an g e n t y = \frac{1}{x}

\int \frac{cos ( x )}{1 + sin ( x )} d x

\int sin (2 x y) d x