$f'(x) = \lim_{{\Delta x \to 0}} \frac{f(x0+\Delta x) - f(x0)}{\Delta x}$
$f(x0+\Delta x) - f(x0) = \Delta y$
$f'(x) = \lim_{{\Delta x \to 0}} \frac{\Delta y}{\Delta x}$
$f'(x)$就是导数
导数粗糙的理解为就是在某点的切线斜率
可导意味着在某点处它的导数存在
微分:
$y=f(x) = 3x, x0->(x0+\Deltax)$
$\Delta y = f(x0+ \Delta x) - f(x0) = 3(x0 + \Delta x) -3x0 = 3\Delta x$
$y = f(x) = x^2 $
$\Delta y = (x0+\Delta x)^2 - (x0)^2 = 2(x0)^2\Delta x + (\Delta x)^2$
如果满足$\Delta x -> 0, \Delay y = A \Delta x + o(\Deltax)$,此时称这个函数在这一点可微。
$f(x0+\Delta x) - f(x0) = A\Delta x + o(\Delta x)$
$(f(x0+\Delta x) - f(x0)) / \Delta x = A + o(\Delta x) / \Delta x $
https://www.bilibili.com/video/BV1bW4y1j77v/
$y = f(x)$,
$\Delta y = f(x_0 + \Delta x) - f(x_0)$
设红色为$A\Delta x$,灰色为$o \Delta x$,那么下面会得到:$\Delta y =A\Delta x + o \Delta x$
将$\Delta x$称为自变量的微分,记作$dx$
$dx = \Delta x$
将$A\Delta x$称为函数 $x0$相对于自变量增量$\Delta x$的微分,也就是函数值的微分,记作$dy$
$dy = A\Delta x$
$dy + o \Delta x = \Delta y$
$dy = A(dx)$
A就是导数了,也就是函数在某点的变化率
$f'(x)$是导数
$dy = f'(x) dx$
$f'(x)=\frac{dy}{dx}$
https://www.bilibili.com/video/BV1PL411W7Mu/
https://www.bilibili.com/video/BV1Ja411x7fB/
https://www.bilibili.com/video/BV1sp4y1Y7uz/
标签:P98,导数,Delta,P94,P95,微分,dx,dy,x0 From: https://www.cnblogs.com/xzit201802/p/17707499.html