derivative of (4x^{ln(4x)})

Lösung

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

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

Schritte zur Lösung

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

Wende Exponentenregel an:

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

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

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

Wende die Kettenregel an:

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

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

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

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

Vereinfache

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

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

x \to 6 lim (\frac{4}{x - 6})

t a y l or 9 ln (5 - 8 x^{2})

\int 3 t cos (2 t) d t

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x \to 3 - lim (\frac{7 - x}{x - 3})