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Beliebt Rechnen >

implicit (dy)/(dx),6x^2+3xy+2y^2+17y-6=0

Lösung

implizite ableitung

\frac{d y}{d x}, 6 x^{2} + 3 x y + 2 y^{2} + 17 y - 6 = 0

Lösung

\frac{d y}{d x} = \frac{- 12 x - 3 y}{4 y + 17 + 3 x}

Schritte zur Lösung

6 x^{2} + 3 x y + 2 y^{2} + 17 y - 6 = 0

Behandle

y

wie

y (x)

Beide Seiten differenzieren:

12 x + 4 y \frac{d y}{d x} + 17 \frac{d y}{d x} + 3 (x \frac{d y}{d x} + y) = 0

Isoliere

\frac{d y}{d x} : \frac{d y}{d x} = \frac{- 12 x - 3 y}{4 y + 17 + 3 x}

\frac{d y}{d x} = \frac{- 12 x - 3 y}{4 y + 17 + 3 x}

Beliebte Beispiele

y^{''}-7y^'+12y=0

y^{^{''}} - 7 y^{^{'}} + 12 y = 0

derivative 2x+1

d er i v a t i v e 2 x + 1

y^{''}-3y^'+18y=0

y^{^{''}} - 3 y^{^{'}} + 18 y = 0

integral of (x-2)(x-3)^6

\int (x - 2) (x - 3)^{6} d x

(\partial)/(\partial x)(4(x-y)e^{4y+2x^2})

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