复合函数fx=expsinxx那么fx的8阶导数在0处的绝对值是多少503050405020

首先，我们需要计算$f(x)$的导数。根据链式法则，我们有：

$$f'(x) = (e^{\sin(x^2)})' = e^{\sin(x^2)} \cdot \cos(x^2) \cdot (x^2)' = 2x \cdot e^{\sin(x^2)} \cdot \cos(x^2)$$

接下来，我们可以依次计算$f'(x)$的高阶导数。每次求导都会多出一个$x$的系数，并且会多出一个$\sin(x^2)$或$\cos(x^2)$的因子。

$$f''(x) = 2e^{\sin(x^2)} \cdot \cos(x^2) - 4x^2e^{\sin(x^2)} \cdot \sin(x^2)$$

$$f'''(x) = 2\cos(x^2)e^{\sin(x^2)} - 8xe^{\sin(x^2)} \cdot \sin(x^2) - 8x^3e^{\sin(x^2)} \cdot \cos(x^2)$$

$$f''''(x) = 2e^{\sin(x^2)} \cdot \cos(x^2) - 16xe^{\sin(x^2)} \cdot \sin(x^2) - 24x^2e^{\sin(x^2)} \cdot \cos(x^2) - 16x^4e^{\sin(x^2)} \cdot \cos(x^2)$$

$$f^{(5)}(x) = 2\cos(x^2)e^{\sin(x^2)} - 24xe^{\sin(x^2)} \cdot \sin(x^2) - 48x^2e^{\sin(x^2)} \cdot \cos(x^2) - 80x^3e^{\sin(x^2)} \cdot \sin(x^2)$$

$$f^{(6)}(x) = 2e^{\sin(x^2)} \cdot \cos(x^2) - 48xe^{\sin(x^2)} \cdot \sin(x^2) - 144x^2e^{\sin(x^2)} \cdot \cos(x^2) - 160x^3e^{\sin(x^2)} \cdot \sin(x^2) - 80x^5e^{\sin(x^2)} \cdot \cos(x^2)$$

$$f^{(7)}(x) = 2\cos(x^2)e^{\sin(x^2)} - 160xe^{\sin(x^2)} \cdot \sin(x^2) - 480x^2e^{\sin(x^2)} \cdot \cos(x^2) - 480x^3e^{\sin(x^2)} \cdot \sin(x^2) - 400x^5e^{\sin(x^2)} \cdot \cos(x^2)$$

$$f^{(8)}(x) = 2e^{\sin(x^2)} \cdot \cos(x^2) - 480xe^{\sin(x^2)} \cdot \sin(x^2) - 1440x^2e^{\sin(x^2)} \cdot \cos(x^2) - 1920x^3e^{\sin(x^2)} \cdot \sin(x^2) - 800x^5e^{\sin(x^2)} \cdot \cos(x^2) - 160x^7e^{\sin(x^2)} \cdot \cos(x^2)$$

现在我们可以计算$f^{(8)}(0)$，即在$x=0$处求$f(x)$的8阶导数：

$$f^{(8)}(0) = 2e^{\sin(0^2)} \cdot \cos(0^2) - 480 \cdot 0 \cdot e^{\sin(0^2)} \cdot \sin(0^2) - 1440 \cdot 0^2 \cdot e^{\sin(0^2)} \cdot \cos(0^2) - 1920 \cdot 0^3 \cdot e^{\sin(0^2)} \cdot \sin(0^2) - 800 \cdot 0^5 \cdot e^{\sin(0^2)} \cdot \cos(0^2) - 160 \cdot 0^7 \cdot e^{\sin(0^2)} \cdot \cos(0^2)$$

化简后得到：

$$f^{(8)}(0) = 2 - 0 - 0 - 0 - 0 - 0 = 2$$

因此，$f(x)$的8阶导数在$x=0$处的绝对值为2。

所以答案是2