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Beliebt Rechnen >

derivative of (sqrt(x)^{5x})

Lösung

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

Lösung

5 x^{\frac{5 x}{2}} (\frac{1}{2} ln (x) + \frac{1}{2})

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) + \frac{1}{2})

= e^{5 x l n (x)} \cdot 5 (ln (x) + \frac{1}{2})

Vereinfache

e^{5 x l n (x)} \cdot 5 (ln (x) + \frac{1}{2}) : 5 x^{\frac{5 x}{2}} (\frac{1}{2} ln (x) + \frac{1}{2})

= 5 x^{\frac{5 x}{2}} (\frac{1}{2} ln (x) + \frac{1}{2})

Graph

Beliebte Beispiele

integral of (x^3+x+4)/(x^2)

\int \frac{x ^{3} + x + 4}{x ^{2}} d x

d/(dy)(arctan(x/y))

\frac{d}{d y} (arctan (\frac{x}{y}))

derivative of \sqrt[8]{x^9}

\frac{d}{d x} (8 x^{9})

derivative of arctan(x^4)

\frac{d}{d x} (arctan (x^{4}))

f(t)=sqrt((t^2+1)/(t^2-1))

f (t) = \frac{t ^{2} + 1}{t ^{2} - 1}