(\partial)/(\partial x)(\sqrt[4]{6x^2+4})

Lösung

\frac{\partial}{\partial x} (4 6 x^{2} + 4)

\frac{3 x}{( 6 x ^{2} + 4 ) ^{\frac{3}{4}}}

Schritte zur Lösung

\frac{\partial}{\partial x} (4 6 x^{2} + 4)

Wende die Kettenregel an:

\frac{1}{4 ( 6 x ^{2} + 4 ) ^{\frac{3}{4}}} \frac{\partial}{\partial x} (6 x^{2} + 4)

= \frac{1}{4 ( 6 x ^{2} + 4 ) ^{\frac{3}{4}}} \frac{\partial}{\partial x} (6 x^{2} + 4)

\frac{\partial}{\partial x} (6 x^{2} + 4) = 12 x

= \frac{1}{4 ( 6 x ^{2} + 4 ) ^{\frac{3}{4}}} \cdot 12 x

Vereinfache

\frac{1}{4 ( 6 x ^{2} + 4 ) ^{\frac{3}{4}}} \cdot 12 x : \frac{3 x}{( 6 x ^{2} + 4 ) ^{\frac{3}{4}}}

= \frac{3 x}{( 6 x ^{2} + 4 ) ^{\frac{3}{4}}}

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