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Beliebt Rechnen >

implicit (dy)/(dx),5xy^5+3xy=24

Lösung

implizite ableitung

\frac{d y}{d x}, 5 x y^{5} + 3 x y = 24

Lösung

\frac{d y}{d x} = \frac{- 5 y ^{5} - 3 y}{x ( 3 + 25 y ^{4} )}

Schritte zur Lösung

5 x y^{5} + 3 x y = 24

Behandle

y

wie

y (x)

Beide Seiten differenzieren:

5 (y^{5} + 5 x y^{4} \frac{d y}{d x}) + 3 (y + x \frac{d y}{d x}) = 0

Isoliere

\frac{d y}{d x} : \frac{d y}{d x} = \frac{- 5 y ^{5} - 3 y}{x ( 3 + 25 y ^{4} )}

\frac{d y}{d x} = \frac{- 5 y ^{5} - 3 y}{x ( 3 + 25 y ^{4} )}

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