implicit (dy)/(dx),ln(x^2-24y)=x-y-4

解答

隐函数求导

\frac{d y}{d x}, ln (x^{2} - 24 y) = x - y - 4

\frac{d y}{d x} = \frac{x ^{2} - 24 y - 2 x}{- 24 + x ^{2} - 24 y}

求解步骤

ln (x^{2} - 24 y) = x - y - 4

将

y

视为

y (x)

对两侧微分:

\frac{2 x - 24 \frac{d y}{d x}}{x ^{2} - 24 y} = - \frac{d y}{d x} + 1

整理

\frac{d y}{d x} : \frac{d y}{d x} = \frac{x ^{2} - 24 y - 2 x}{- 24 + x ^{2} - 24 y}

\frac{d y}{d x} = \frac{x ^{2} - 24 y - 2 x}{- 24 + x ^{2} - 24 y}

t an g e n t f (x) = - 2 - 6 x^{2}, (5, - 152)

in v erse l a pl a ce \frac{3 s - 4}{s ^{2} + 4 s + 8}

x \to 1 - 0 lim (\frac{1}{1 - x})

x \to \infty + lim (x ln (x))

d er i v a t i v e f (x) = x^{3} - 7 x^{2} + 6 x + 1