implicit (dy)/(dx),arctan(xy)=arcsin(2x+2y),(0,0)

解答

隐函数求导

\frac{d y}{d x}, arctan (x y) = arcsin (2 x + 2 y), (0, 0)

- 1

求解步骤

arctan (x y) = arcsin (2 x + 2 y)

隐函数

arctan (x y) = arcsin (2 x + 2 y)

的导数:

\frac{2 x ^{2} y ^{2} + 2 - y 1 - 4 x ^{2} - 8 x y - 4 y ^{2}}{x 1 - 4 y ^{2} - 4 x ^{2} - 8 x y - 2 x ^{2} y ^{2} - 2}

替代

x = 0, y = 0 : - 1

= - 1

2 t y^{^{'}} - 4 y = 4 t^{4} e^{t^{2}}

\frac{\partial}{\partial x} (4 e^{5 x y})

x \to + 0 lim (\frac{1}{csc ( x )})

\int \frac{1}{100 x ^{2} + 1} d x

y^{^{'}} = \frac{y}{x} + \frac{6 x ^{3}}{y} cos (x^{2})