(\partial)/(\partial x)(sqrt((x+4)/(y+4)))

解答

\frac{\partial}{\partial x} (\frac{x + 4}{y + 4})

\frac{1}{2 x + 4 y + 4}

求解步骤

\frac{\partial}{\partial x} (\frac{x + 4}{y + 4})

将

y

视为常数

使用连锁律:

\frac{1}{2 \frac{x + 4}{y + 4}} \frac{\partial}{\partial x} (\frac{x + 4}{y + 4})

= \frac{1}{2 \frac{x + 4}{y + 4}} \frac{\partial}{\partial x} (\frac{x + 4}{y + 4})

\frac{\partial}{\partial x} (\frac{x + 4}{y + 4}) = \frac{1}{y + 4}

= \frac{1}{2 \frac{x + 4}{y + 4}} \cdot \frac{1}{y + 4}

化简

\frac{1}{2 \frac{x + 4}{y + 4}} \cdot \frac{1}{y + 4} : \frac{1}{2 x + 4 y + 4}

= \frac{1}{2 x + 4 y + 4}

\int \frac{1}{2 - cos ( x )} d x

\frac{\partial}{\partial x} (2 x + 2 y)

\frac{\partial}{\partial x} (9 x + y + 7 x y)

f^{^{'}} (x) = 1 - 2 x

x \to \infty lim (x^{2} + 5 x)