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Beliebt Rechnen >

implicit (dy)/(dx),(4x+4y)3=64x^3+64y^3

Lösung

implizite ableitung

\frac{d y}{d x}, (4 x + 4 y) 3 = 64 x^{3} + 64 y^{3}

Lösung

\frac{d y}{d x} = \frac{16 x ^{2} - 1}{1 - 16 y ^{2}}

Schritte zur Lösung

(4 x + 4 y) \cdot 3 = 64 x^{3} + 64 y^{3}

Behandle

y

wie

y (x)

Beide Seiten differenzieren:

3 (4 + 4 \frac{d y}{d x}) = 192 x^{2} + 192 y^{2} \frac{d y}{d x}

Isoliere

\frac{d y}{d x} : \frac{d y}{d x} = \frac{16 x ^{2} - 1}{1 - 16 y ^{2}}

\frac{d y}{d x} = \frac{16 x ^{2} - 1}{1 - 16 y ^{2}}

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