derivative of x^{tan(x})

Lösung

\frac{d}{d x} (x^{t a n (x)})

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

Schritte zur Lösung

\frac{d}{d x} (x^{t a n (x)})

Wende Exponentenregel an:

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

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

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

Wende die Kettenregel an:

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

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

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

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

\int_{1}^{9} \frac{2}{x} d x

\frac{d}{d x} (\frac{2}{3} x^{2} (x^{3} - 1))

\int (x^{3} + x^{2} - x) d x

\int \frac{cos ( x )}{9 - sin ( x )} d x

\frac{d}{d x} (3 x (10 x^{3} - \frac{6}{x + 10}))