implicit (dy)/(dx),4x^2+5xy-y^2=2

解答

隐函数求导

\frac{d y}{d x}, 4 x^{2} + 5 x y - y^{2} = 2

\frac{d y}{d x} = \frac{- 8 x - 5 y}{5 x - 2 y}

求解步骤

4 x^{2} + 5 x y - y^{2} = 2

将

y

视为

y (x)

对两侧微分:

8 x + 5 (y + x \frac{d y}{d x}) - 2 y \frac{d y}{d x} = 0

整理

\frac{d y}{d x} : \frac{d y}{d x} = \frac{- 8 x - 5 y}{5 x - 2 y}

\frac{d y}{d x} = \frac{- 8 x - 5 y}{5 x - 2 y}

l a pl a ce t r an s f or m - 3 sin (4 t)

x \cdot \frac{d y}{d x} - x^{2} + x \cdot e^{- x} = 0

\frac{d}{d x} (\frac{x ^{5}}{5})

\frac{d}{d x} (\frac{6}{x + 1})

\frac{d}{d x} (cosh (x) - (2 e^{(- 0.3 x)}))