derivative of (3+tan(x)^x)

Lösung

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

(ln (3 + tan (x)) + \frac{x sec ^{2} ( x )}{3 + tan ( x )}) (3 + tan (x))^{x}

Schritte zur Lösung

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

Wende Exponentenregel an:

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

(3 + tan (x))^{x} = e^{x l n (3 + t a n (x))}

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

Wende die Kettenregel an:

e^{x l n (3 + t a n (x))} \frac{d}{d x} (x ln (3 + tan (x)))

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

\frac{d}{d x} (x ln (3 + tan (x))) = ln (3 + tan (x)) + \frac{x sec ^{2} ( x )}{3 + tan ( x )}

= e^{x l n (3 + t a n (x))} (ln (3 + tan (x)) + \frac{x sec ^{2} ( x )}{3 + tan ( x )})

e^{x l n (3 + t a n (x))} = (3 + tan (x))^{x}

= (ln (3 + tan (x)) + \frac{x sec ^{2} ( x )}{3 + tan ( x )}) (3 + tan (x))^{x}

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