implicit (dy)/(dx),y=7x^2+6yx

解答

隐函数求导

\frac{d y}{d x}, y = 7 x^{2} + 6 y x

\frac{d y}{d x} = \frac{14 x + 6 y}{1 - 6 x}

求解步骤

y = 7 x^{2} + 6 y x

将

y

视为

y (x)

对两侧微分:

\frac{d y}{d x} = 14 x + 6 (x \frac{d y}{d x} + y)

整理

\frac{d y}{d x} : \frac{d y}{d x} = \frac{14 x + 6 y}{1 - 6 x}

\frac{d y}{d x} = \frac{14 x + 6 y}{1 - 6 x}

\int e^{- θ} cos (8 θ) d θ

\frac{\partial}{\partial x} (\frac{1}{x y ^{2} - x ^{2} y})

x \to 0 lim ((e^{x} + x)^{\frac{1}{x}})

(x + 1) \frac{d y}{d x} + y = x ln^{2} (x)

x \to \infty lim (\frac{( ln ( e ^{3 x} + x ) )}{x})