implicit (dy)/(dx),y*cos(x)=2x^2+5y^2

解答

隐函数求导

\frac{d y}{d x}, y \cdot cos (x) = 2 x^{2} + 5 y^{2}

\frac{d y}{d x} = \frac{4 x + y sin ( x )}{cos ( x ) - 10 y}

求解步骤

y cos (x) = 2 x^{2} + 5 y^{2}

将

y

视为

y (x)

对两侧微分:

cos (x) \frac{d y}{d x} - sin (x) y = 4 x + 10 y \frac{d y}{d x}

整理

\frac{d y}{d x} : \frac{d y}{d x} = \frac{4 x + y sin ( x )}{cos ( x ) - 10 y}

\frac{d y}{d x} = \frac{4 x + y sin ( x )}{cos ( x ) - 10 y}

\int_{5}^{8} \frac{x}{x ^{2} + 6 x + 13} d x

\int_{\frac{1}{7}}^{5} 14 x ln (7 x) d x

\int_{1}^{4} \frac{x ^{2} + 6}{5 x - x ^{2}} d x

\int x^{7} sin (1 + x^{\frac{9}{2}}) d x

x \to - \infty lim (2^{x} + 3)