implicit (dy)/(dx),6x^3+7y^3=13xy

解答

隐函数求导

\frac{d y}{d x}, 6 x^{3} + 7 y^{3} = 13 x y

\frac{d y}{d x} = \frac{13 y - 18 x ^{2}}{21 y ^{2} - 13 x}

求解步骤

6 x^{3} + 7 y^{3} = 13 x y

将

y

视为

y (x)

对两侧微分:

18 x^{2} + 21 y^{2} \frac{d y}{d x} = 13 (y + x \frac{d y}{d x})

整理

\frac{d y}{d x} : \frac{d y}{d x} = \frac{13 y - 18 x ^{2}}{21 y ^{2} - 13 x}

\frac{d y}{d x} = \frac{13 y - 18 x ^{2}}{21 y ^{2} - 13 x}

s l o p e in t erce pt (- 1.4) (1.4)

\int sin (x) d x

f (x) = x^{4} e^{x}

ma c l a u r in \frac{1}{1 - t}

\frac{d}{d x} ((4 + 2 x^{2})^{7})