derivative of (tan(x)^x)

Lösung

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

tan^{x} (x) (ln (tan (x)) + 2 x csc (2 x))

Schritte zur Lösung

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

Wende Exponentenregel an:

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

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

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

Wende die Kettenregel an:

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

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

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

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

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

= tan^{x} (x) (ln (tan (x)) + 2 x csc (2 x))

\frac{d y}{d x} = \frac{cos ( 6 x )}{e ^{6 y}}

\frac{d y}{d x} = \frac{3 x}{y + x ^{2} y}

\frac{\partial}{\partial x} (\frac{x - y}{x ^{2} + y ^{2}})

\int \frac{1 - x}{x ^{2} + 3 x + 2} d x

\frac{d}{d x} (x e^{x} sin (2 x))