derivative of (sqrt(x)^{3x})

Lösung

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

3 x^{\frac{3 x}{2}} (\frac{1}{2} ln (x) + \frac{1}{2})

Schritte zur Lösung

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

Wende Exponentenregel an:

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

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

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

Wende die Kettenregel an:

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

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

\frac{d}{d x} (3 x ln (x)) = 3 (ln (x) + \frac{1}{2})

= e^{3 x l n (x)} \cdot 3 (ln (x) + \frac{1}{2})

Vereinfache

e^{3 x l n (x)} \cdot 3 (ln (x) + \frac{1}{2}) : 3 x^{\frac{3 x}{2}} (\frac{1}{2} ln (x) + \frac{1}{2})

= 3 x^{\frac{3 x}{2}} (\frac{1}{2} ln (x) + \frac{1}{2})

\int \frac{1}{( 4 x + 1 ) ^{3}} d x

y \cdot \frac{d y}{d x} - x = 5 y^{2}

\frac{d}{d x} (ln ((x^{2} - 1)^{3}))

\frac{\partial}{\partial x} (- x sin (y))

in v erse l a pl a ce \frac{1}{s ( s ^{2} + 0.2 s + 1 )}