derivative of (d/(dx(x^3))^2)

Lösung

\frac{d}{d x} ((\frac{d}{d x} (x^{3}))^{2})

36 x^{3}

Schritte zur Lösung

\frac{d}{d x} ((\frac{d}{d x} (x^{3}))^{2})

Wende die Kettenregel an:

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

= 2 \frac{d}{d x} (x^{3}) \frac{d}{d x} (\frac{d}{d x} (x^{3}))

\frac{d}{d x} (\frac{d}{d x} (x^{3})) = 6 x

= 2 \frac{d}{d x} (x^{3}) 6 x

Wende die Potenzregel an:

\frac{d}{d x} (x^{a}) = a \cdot x^{a - 1}

= 2 \cdot 3 x^{3 - 1} \cdot 6 x

Vereinfache

2 \cdot 3 x^{3 - 1} \cdot 6 x : 36 x^{3}

= 36 x^{3}

\frac{d}{d x} (3 x^{2} - 4 x + 2)

\frac{d y}{d x} + y = e^{6 x}

\frac{d}{d x} (cos^{2} (sin (2 x)))

\frac{d}{d x} ((x^{2} + 1)^{l n (x)})

i = 1 \sum \infty 4 (2)^{i - 1}