derivative of (1+3/x ^x)

Lösung

\frac{d}{d x} ((1 + \frac{3}{x})^{x})

(ln (1 + \frac{3}{x}) - \frac{3}{x + 3}) (1 + \frac{3}{x})^{x}

Schritte zur Lösung

\frac{d}{d x} ((1 + \frac{3}{x})^{x})

Wende Exponentenregel an:

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

(1 + \frac{3}{x})^{x} = e^{x l n (1 + \frac{3}{x})}

= \frac{d}{d x} (e^{x l n (1 + \frac{3}{x})})

Wende die Kettenregel an:

e^{x l n (1 + \frac{3}{x})} \frac{d}{d x} (x ln (1 + \frac{3}{x}))

= e^{x l n (1 + \frac{3}{x})} \frac{d}{d x} (x ln (1 + \frac{3}{x}))

\frac{d}{d x} (x ln (1 + \frac{3}{x})) = ln (1 + \frac{3}{x}) - \frac{3}{x + 3}

= e^{x l n (1 + \frac{3}{x})} (ln (1 + \frac{3}{x}) - \frac{3}{x + 3})

e^{x l n (1 + \frac{3}{x})} = (1 + \frac{3}{x})^{x}

= (ln (1 + \frac{3}{x}) - \frac{3}{x + 3}) (1 + \frac{3}{x})^{x}

\frac{\partial}{\partial x} ((ln (x))^{2})

\int \frac{x ^{3} + x ^{2} - x ^{5}}{x ^{6}} d x

\frac{d}{d x} (\frac{1}{4} (x^{4} + 8))

d er i v a t i v e g (x) = 3 x^{4} - 140 x^{3}

\int \frac{1}{t} d t