derivative of (x+2^x)

Lösung

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

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

Schritte zur Lösung

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

Wende Exponentenregel an:

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

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

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

Wende die Kettenregel an:

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

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

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

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

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

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

\int \frac{( 2 + e ^{x} ) ^{2}}{e ^{x}} d x

x y^{^{'}} + 3 y = x^{4} - x

\int \frac{e ^{x}}{( 5 - e ^{x} ) ^{2}} d x

\int \frac{1}{v ^{2} - v + 1} d v

d er i v a t i v e f (x) = ln (\frac{x + 1}{x - 1})