derivative of (6x^3+7^{3/2})

Lösung

\frac{d}{d x} ((6 x^{3} + 7)^{\frac{3}{2}})

27 x^{2} (6 x^{3} + 7)^{\frac{1}{2}}

Schritte zur Lösung

\frac{d}{d x} ((6 x^{3} + 7)^{\frac{3}{2}})

Wende die Kettenregel an:

\frac{3 ( 6 x ^{3} + 7 ) ^{\frac{1}{2}}}{2} \frac{d}{d x} (6 x^{3} + 7)

= \frac{3 ( 6 x ^{3} + 7 ) ^{\frac{1}{2}}}{2} \frac{d}{d x} (6 x^{3} + 7)

\frac{d}{d x} (6 x^{3} + 7) = 18 x^{2}

= \frac{3 ( 6 x ^{3} + 7 ) ^{\frac{1}{2}}}{2} \cdot 18 x^{2}

Vereinfache

\frac{3 ( 6 x ^{3} + 7 ) ^{\frac{1}{2}}}{2} \cdot 18 x^{2} : 27 x^{2} (6 x^{3} + 7)^{\frac{1}{2}}

= 27 x^{2} (6 x^{3} + 7)^{\frac{1}{2}}

l a pl a ce t r an s f or m 5 cos (3 t)

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