复合函数fx=expsinx^2那么fx的8阶导数在0处的绝对值是多少

首先，我们可以计算出f(x)的一阶导数：

f'(x) = (exp(sinx^2))' = exp(sinx^2) * (sinx^2)' = 2sinx * exp(sinx^2)

然后，我们可以计算出f(x)的二阶导数：

f''(x) = (2sinx * exp(sinx^2))' = 2cosx * exp(sinx^2) + 2sinx * exp(sinx^2) * (sinx^2)' = 2cosx * exp(sinx^2) + 4sin^2x * exp(sinx^2)

接下来，我们可以计算出f(x)的三阶导数：

f'''(x) = (2cosx * exp(sinx^2) + 4sin^2x * exp(sinx^2))' = -2sinx * exp(sinx^2) + 2cos^2x * exp(sinx^2) + 8sinxcosx * exp(sinx^2) + 8sin^3x * exp(sinx^2) * (sinx^2)'

继续计算四阶导数：

f''''(x) = (-2sinx * exp(sinx^2) + 2cos^2x * exp(sinx^2) + 8sinxcosx * exp(sinx^2) + 8sin^3x * exp(sinx^2) * (sinx^2)')' = -2cosx * exp(sinx^2) - 4sinx * cosx * exp(sinx^2) + 4cos^3x * exp(sinx^2) + 8cos^2x * sinx * exp(sinx^2) + 24sin^2x * cosx * exp(sinx^2) + 16sin^4x * exp(sinx^2) * (sinx^2)'

继续计算五阶导数：

f'''''(x) = (-2cosx * exp(sinx^2) - 4sinx * cosx * exp(sinx^2) + 4cos^3x * exp(sinx^2) + 8cos^2x * sinx * exp(sinx^2) + 24sin^2x * cosx * exp(sinx^2) + 16sin^4x * exp(sinx^2) * (sinx^2)')' = 2sinx * exp(sinx^2) - 6sinx * cos^2x * exp(sinx^2) - 12sin^2x * cosx * exp(sinx^2) + 12sinx * cos^4x * exp(sinx^2) + 48sin^2x * cos^2x * exp(sinx^2) + 16sin^5x * exp(sinx^2) * (sinx^2)' + 32sin^3x * exp(sinx^2) * (sinx^2)''

接下来，我们可以计算六阶导数：

f''''''(x) = (2sinx * exp(sinx^2) - 6sinx * cos^2x * exp(sinx^2) - 12sin^2x * cosx * exp(sinx^2) + 12sinx * cos^4x * exp(sinx^2) + 48sin^2x * cos^2x * exp(sinx^2) + 16sin^5x * exp(sinx^2) * (sinx^2)' + 32sin^3x * exp(sinx^2) * (sinx^2)'')' = 2cosx * exp(sinx^2) - 2sinx * cos^2x * exp(sinx^2) - 16sin^2x * cosx * exp(sinx^2) - 12sinx * cos^4x * exp(sinx^2) + 96sin^2x * cos^2x * exp(sinx^2) + 32sin^5x * exp(sinx^2) * (sinx^2)' + 32sin^3x * exp(sinx^2) * (sinx^2)'' + 64sin^4x * exp(sinx^2) * (sinx^2)''

再计算七阶导数：

f'''''''(x) = (2cosx * exp(sinx^2) - 2sinx * cos^2x * exp(sinx^2) - 16sin^2x * cosx * exp(sinx^2) - 12sinx * cos^4x * exp(sinx^2) + 96sin^2x * cos^2x * exp(sinx^2) + 32sin^5x * exp(sinx^2) * (sinx^2)' + 32sin^3x * exp(sinx^2) * (sinx^2)'' + 64sin^4x * exp(sinx^2) * (sinx^2)'')' = -2sinx * exp(sinx^2) - 2cos^2x * exp(sinx^2) + 4sinx * cos^2x * exp(sinx^2) + 32sinx * cosx * exp(sinx^2) - 32sin^3x * cos^2x * exp(sinx^2) + 192sinx * sin^3x * cosx * exp(sinx^2) + 48sin^5x * cosx * exp(sinx^2) + 32sin^3x * exp(sinx^2) * (sinx^2)'' + 64sin^4x * exp(sinx^2) * (sinx^2)'' + 128sin^3x * sinx^2 * exp(sinx^2) * (sinx^2)'' + 128sin^5x * exp(sinx^2) * (sinx^2)'' + 256sin^4x * sinx^2 * exp(sinx^2) * (sinx^2)''

最后，计算八阶导数：

f''''''''(x) = (-2sinx * exp(sinx^2) - 2cos^2x * exp(sinx^2) + 4sinx * cos^2x * exp(sinx^2) + 32sinx * cosx * exp(sinx^2) - 32sin^3x * cos^2x * exp(sinx^2) + 192sinx * sin^3x * cosx * exp(sinx^2) + 48sin^5x * cosx * exp(sinx^2) + 32sin^3x * exp(sinx^2) * (sinx^2)'' + 64sin^4x * exp(sinx^2) * (sinx^2)'' + 128sin^3x * sinx^2 * exp(sinx^2) * (sinx^2)'' + 128sin^5x * exp(sinx^2) * (sinx^2)'' + 256sin^4x * sinx^2 * exp(sinx^2) * (sinx^2)'')' = -2cosx * exp(sinx^2) + 4sinx * cos^2x * exp(sinx^2) + 4sin^2x * cos^2x * exp(sinx^2) - 8sinx * cos^2x * exp(sinx^2) + 32cos^3x * sinx * exp(sinx^2) + 96sin^3x * cosx * exp(sinx^2) - 96sin^3x * cos^3x * exp(sinx^2) + 240sinx * sin^3x * cosx * exp(sinx^2) + 48sin^5x * cosx * exp(sinx^2) + 32sin^3x * exp(sinx^2) * (sinx^2)'' + 64sin^4x * exp(sinx^2) * (sinx^2)'' + 128sin^3x * sinx^2 * exp(sinx^2) * (sinx^2)'' + 128sin^5x * exp(sinx^2) * (sinx^2)'' + 256sin^4x * sinx^2 * exp(sinx^2) * (sinx^2)''

将x=0代入上式，可以得到f''''''''(0)的值