derivative of \sqrt[4]{y-2x}

解答

\frac{d}{d x} (4 y - 2 x)

\frac{\frac{d y}{d x} - 2}{4 ( y - 2 x ) ^{\frac{3}{4}}}

求解步骤

\frac{d}{d x} (4 y - 2 x)

使用连锁律:

\frac{1}{4 ( y - 2 x ) ^{\frac{3}{4}}} \frac{d}{d x} (y - 2 x)

= \frac{1}{4 ( y - 2 x ) ^{\frac{3}{4}}} \frac{d}{d x} (y - 2 x)

\frac{d}{d x} (y - 2 x) = \frac{d y}{d x} - 2

= \frac{1}{4 ( y - 2 x ) ^{\frac{3}{4}}} (\frac{d y}{d x} - 2)

化简

\frac{1}{4 ( y - 2 x ) ^{\frac{3}{4}}} (\frac{d y}{d x} - 2) : \frac{\frac{d y}{d x} - 2}{4 ( y - 2 x ) ^{\frac{3}{4}}}

= \frac{\frac{d y}{d x} - 2}{4 ( y - 2 x ) ^{\frac{3}{4}}}

d er i v a t i v e f (x) = 3 36 x^{2} + 10

\frac{\partial}{\partial x} (- 2 x - 8 y + 18)

\frac{d}{d x} (cos (arccos (x)))

\frac{d}{d x} (\frac{1}{2} (x - \frac{1}{2} sin (2 x)))

d er i v a t i v e (\frac{x + 3}{x - 2})^{3}