(参考)「コンピューターでの微分」
http://qiita.com/namitop/items/55536bbbd5f92d18b2a0
from sympy import *
var('x')
y=0.01*x**2 + 0.1*x
yd=diff(y,x)
print(type(y),y)
print(type(yd),yd)
input={x:5}
print(yd.subs(input))
input={x:10}
print(yd.subs(input))
print('-----------------------------')
print(diff(0.01*x**2+0.1*x).subs([(x, 5)]))
print(diff(0.01*x**2+0.1*x).subs([(x,10)]))
# <class 'sympy.core.add.Add'> 0.01*x**2 + 0.1*x
# <class 'sympy.core.add.Add'> 0.02*x + 0.1
# 0.200000000000000
# 0.300000000000000
# 0.200000000000000
# 0.300000000000000
--------------
【補足】(2017/06/12)リンクが途中で切れています。
(参考)Wolfram|Alpha: Computational Knowledge Engine>derivative 0.01*x*2 + 0.1*x
http://www.wolframalpha.com/input/?i=derivative+0.01*x2+%2B+0.1*x
0.1 + 0.02 x
(参考)Wolfram|Alpha: Computational Knowledge Engine>derivative 0.01*x2 + 0.1*x,x=5
http://www.wolframalpha.com/input/?i=derivative+0.01*x2+%2B+0.1*x,x%3D5
0.2
(参考)Wolfram|Alpha: Computational Knowledge Engine>derivative 0.01*x2 + 0.1*x,x=10
http://www.wolframalpha.com/input/?i=derivative+0.01*x*2+%2B+0.1*x,x%3D10
0.3