(d^2)/(dx^2)(x^3+y^3)

Lösung

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

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

Schritte zur Lösung

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

\frac{d}{d x} (x^{3} + y^{3}) = 3 x^{2} + 3 y^{2} \frac{d y}{d x}

= \frac{d}{d x} (3 x^{2} + 3 y^{2} \frac{d y}{d x})

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

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

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