## 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 . . .