derivative (a+3y^2+b)^{1/2}

Lösung

ableitung von

(a + 3 y^{2} + b)^{\frac{1}{2}}

\frac{3 y}{( a + 3 y ^{2} + b ) ^{\frac{1}{2}}}

Schritte zur Lösung

\frac{d}{d y} ((a + 3 y^{2} + b)^{\frac{1}{2}})

Wende die Kettenregel an:

\frac{1}{2 ( a + 3 y ^{2} + b ) ^{\frac{1}{2}}} \frac{d}{d y} (a + 3 y^{2} + b)

= \frac{1}{2 ( a + 3 y ^{2} + b ) ^{\frac{1}{2}}} \frac{d}{d y} (a + 3 y^{2} + b)

\frac{d}{d y} (a + 3 y^{2} + b) = 6 y

= \frac{1}{2 ( a + 3 y ^{2} + b ) ^{\frac{1}{2}}} \cdot 6 y

Vereinfache

\frac{1}{2 ( a + 3 y ^{2} + b ) ^{\frac{1}{2}}} \cdot 6 y : \frac{3 y}{( a + 3 y ^{2} + b ) ^{\frac{1}{2}}}

= \frac{3 y}{( a + 3 y ^{2} + b ) ^{\frac{1}{2}}}

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