implicit (dy)/(dx),(3xy+7)^2=6y

解答

隐函数求导

\frac{d y}{d x}, (3 x y + 7)^{2} = 6 y

\frac{d y}{d x} = - \frac{y ( 3 x y + 7 )}{3 x ^{2} y + 7 x - 1}

求解步骤

(3 x y + 7)^{2} = 6 y

将

y

视为

y (x)

对两侧微分:

6 (3 x y + 7) (x \frac{d y}{d x} + y) = 6 \frac{d y}{d x}

整理

\frac{d y}{d x} : \frac{d y}{d x} = - \frac{y ( 3 x y + 7 )}{3 x ^{2} y + 7 x - 1}

\frac{d y}{d x} = - \frac{y ( 3 x y + 7 )}{3 x ^{2} y + 7 x - 1}

\int \frac{3}{8} x^{2} d x

a re a y = x, y = x - 2, y = 0

t an g e n t f (x) = 3 x^{- 2}, at x = 4

\int_{0}^{π^{2}} sin (x) d x

d er i v a t i v e 3 x^{\frac{1}{3}} - 5 x^{\frac{4}{3}}