implicit (dy)/(dx),5cos(xy)=6x+7y

解答

隐函数求导

\frac{d y}{d x}, 5 cos (x y) = 6 x + 7 y

\frac{d y}{d x} = - \frac{6 + 5 y sin ( x y )}{7 + 5 x sin ( x y )}

求解步骤

5 cos (x y) = 6 x + 7 y

将

y

视为

y (x)

对两侧微分:

- 5 sin (x y) (y + x \frac{d y}{d x}) = 6 + 7 \frac{d y}{d x}

整理

\frac{d y}{d x} : \frac{d y}{d x} = - \frac{6 + 5 y sin ( x y )}{7 + 5 x sin ( x y )}

\frac{d y}{d x} = - \frac{6 + 5 y sin ( x y )}{7 + 5 x sin ( x y )}

\int cos^{4} (3 t) d t

\int_{- π}^{π} x d x

\frac{d ^{2} y}{d x ^{2}} + 5 \frac{d y}{d x} + 6 y = 12 e^{x}

y^{^{'}} + 100 y = 0

n = 1 \sum \infty 2^{n} \cdot 3^{- n}