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Beliebt Rechnen >

derivative x^{5x}

Lösung

ableitung von

x^{5 x}

Lösung

5 x^{5 x} (ln (x) + 1)

Schritte zur Lösung

\frac{d}{d x} (x^{5 x})

Wende Exponentenregel an:

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

x^{5 x} = e^{5 x l n (x)}

= \frac{d}{d x} (e^{5 x l n (x)})

Wende die Kettenregel an:

e^{5 x l n (x)} \frac{d}{d x} (5 x ln (x))

= e^{5 x l n (x)} \frac{d}{d x} (5 x ln (x))

\frac{d}{d x} (5 x ln (x)) = 5 (ln (x) + 1)

= e^{5 x l n (x)} \cdot 5 (ln (x) + 1)

e^{5 x l n (x)} = x^{5 x}

= 5 x^{5 x} (ln (x) + 1)

Graph

Beliebte Beispiele

integral of 12e^{2t}

\int 12 e^{2 t} d t

tangent y=sqrt(1-4x),\at x=-1

t an g e n t y = 1 - 4 x, at x = - 1

integral of \sqrt[3]{3x+2}

\int 3 3 x + 2 d x

integral of 1/((16x^2+9)^2)

\int \frac{1}{( 16 x ^{2} + 9 ) ^{2}} d x

tangent 7/x ,\at x=6

t an g e n t \frac{7}{x}, at x = 6