Exercise 2.56 · 习题

Exercise 2.56: Show how to extend the basic
differentiator to handle more kinds of expressions. For instance, implement
the differentiation rule
d
(

u

n

)

d
x

=

n

u

n
−
1

d
u

d

x

by adding a new clause to the deriv program and defining appropriate

procedures exponentiation?, base, exponent, and

make-exponentiation. (You may use the symbol ** to denote

exponentiation.) Build in the rules that anything raised to the power 0 is 1

and anything raised to the power 1 is the thing itself.

练习 2.56：说明如何扩展基本微分器以处理更多种类的表达式。例如，通过向 deriv 程序添加新的子句并定义适当的过程 exponentiation?、base、exponent 和 make-exponentiation，实现微分规则

d(u^n)/dx = n·u^(n-1)·(du/dx)。（可以用符号 ** 表示乘幂。）内置如下规则：任何数的 0 次幂为 1，任何数的 1 次幂为其本身。