derivative of 3^{xln(x})

Lösung

\frac{d}{d x} (3^{x l n (x)})

ln (3) x^{l n (3) x} (ln (x) + 1)

Schritte zur Lösung

\frac{d}{d x} (3^{x l n (x)})

Wende Exponentenregel an:

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

3^{x l n (x)} = e^{x l n (x) l n (3)}

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

Wende die Kettenregel an:

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

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

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

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

e^{x l n (x) l n (3)} = x^{l n (3) x}

= ln (3) x^{l n (3) x} (ln (x) + 1)

d er i v a t i v e lo g_{e} (sin (2 x) + cot (2 x))

d er i v a t i v e y = \frac{1}{2} x

\int_{π}^{2 π} (t - π) e^{- s t} d t

d er i v a t i v e 13 - x^{2}

\frac{\partial}{\partial y} (3 arctan (\frac{x}{y}))