derivative of sqrt(2x^2+2y^2)

Lösung

\frac{d}{d x} (2 x^{2} + 2 y^{2})

\frac{2 ( x + y \frac{d y}{d x} )}{2 x ^{2} + 2 y ^{2}}

Schritte zur Lösung

\frac{d}{d x} (2 x^{2} + 2 y^{2})

Wende die Kettenregel an:

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

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

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

= \frac{1}{2 2 x ^{2} + 2 y ^{2}} (4 x + 4 y \frac{d y}{d x})

Vereinfache

\frac{1}{2 2 x ^{2} + 2 y ^{2}} (4 x + 4 y \frac{d y}{d x}) : \frac{2 ( x + y \frac{d y}{d x} )}{2 x ^{2} + 2 y ^{2}}

= \frac{2 ( x + y \frac{d y}{d x} )}{2 x ^{2} + 2 y ^{2}}

\int_{- 2}^{4} 10 + 4 x - 3 x^{3} d x

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