ABSTRACT
If y/xn , find dy
dx and
dx
dy :
Solution
From the definition of a derivative:
dy
dx
d
dx [xn] lim
(x h)n xn
h
:
However, expanding (x/h)n by the binomial theorem, and retaining only the first few powers of h because we are only interested in the case when h0/0, gives
d
dx [xn] lim
xn nxn1h
n(n 1)
2! xn2h2 . . .
