derivative of \sqrt[4]{x}^{ln(x})

Lösung

\frac{d}{d x} (4 x^{l n (x)})

\frac{e ^{\frac{l n ^{2} ( x )}{4}} ln ( x )}{2 x}

Schritte zur Lösung

\frac{d}{d x} ((4 x)^{l n (x)})

Wende Exponentenregel an:

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

(4 x)^{l n (x)} = e^{l n (x) l n (4 x)}

= \frac{d}{d x} (e^{l n (x) l n (4 x)})

Wende die Kettenregel an:

e^{l n (x) l n (4 x)} \frac{d}{d x} (ln (x) ln (4 x))

= e^{l n (x) l n (4 x)} \frac{d}{d x} (ln (x) ln (4 x))

\frac{d}{d x} (ln (x) ln (4 x)) = \frac{ln ( x ^{2} )}{4 x}

= e^{l n (x) l n (4 x)} \frac{ln ( x ^{2} )}{4 x}

Vereinfache

e^{l n (x) l n (4 x)} \frac{ln ( x ^{2} )}{4 x} : \frac{e ^{\frac{l n ^{2} ( x )}{4}} ln ( x )}{2 x}

= \frac{e ^{\frac{l n ^{2} ( x )}{4}} ln ( x )}{2 x}

x \to - \infty lim (\frac{- 3 x ^{3} - 4 x ^{2} + 2}{5 x ^{3} + 4 x ^{2} - 2 x})

\frac{d}{d x} (e^{- x} (a cos (x) + b sin (x)))

x \to - \infty lim (\frac{7 x ^{4} - 14 x ^{2}}{6 x ^{5} + 3})

\frac{d}{d x} (sin (\frac{5}{2} ln (x)))

\int \frac{sin ( k t )}{a + cos ( k t )} d t