(\partial)/(\partial x)(4sqrt(y^2+7x^2))

Lösung

\frac{\partial}{\partial x} (4 y^{2} + 7 x^{2})

\frac{28 x}{y ^{2} + 7 x ^{2}}

Schritte zur Lösung

\frac{\partial}{\partial x} (4 y^{2} + 7 x^{2})

Behandle

y

als Konstante

Entferne die Konstante:

(a \cdot f)^{'} = a \cdot f^{'}

= 4 \frac{\partial}{\partial x} (y^{2} + 7 x^{2})

Wende die Kettenregel an:

\frac{1}{2 y ^{2} + 7 x ^{2}} \frac{\partial}{\partial x} (y^{2} + 7 x^{2})

= \frac{1}{2 y ^{2} + 7 x ^{2}} \frac{\partial}{\partial x} (y^{2} + 7 x^{2})

\frac{\partial}{\partial x} (y^{2} + 7 x^{2}) = 14 x

= 4 \cdot \frac{1}{2 y ^{2} + 7 x ^{2}} \cdot 14 x

Vereinfache

4 \cdot \frac{1}{2 y ^{2} + 7 x ^{2}} \cdot 14 x : \frac{28 x}{y ^{2} + 7 x ^{2}}

= \frac{28 x}{y ^{2} + 7 x ^{2}}

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