implicit 3x^2+xy+3y^2=7

Lösung

implizite ableitung

3 x^{2} + x y + 3 y^{2} = 7

\frac{d y}{d x} = \frac{- 6 x - y}{x + 6 y}

Schritte zur Lösung

3 x^{2} + x y + 3 y^{2} = 7

Behandle

y

wie

y (x)

Beide Seiten differenzieren:

6 x + y + x \frac{d y}{d x} + 6 y \frac{d y}{d x} = 0

Isoliere

\frac{d y}{d x} : \frac{d y}{d x} = \frac{- 6 x - y}{x + 6 y}

\frac{d y}{d x} = \frac{- 6 x - y}{x + 6 y}

\int_{1}^{2} 8 x^{3} + 3 x^{2} d x

\frac{\partial}{\partial x} (1 + e^{2 x})

\int_{- 1}^{3} (t + 2) (t^{2} - 2 t + 4) d t

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

a re a f (x) = 2 sin (x) + sin (2 x), y = 0, 0 \leq x \leq π