- #1
madah12
- 326
- 1
Homework Statement
proving the nth derivative of x to the n power is n factorial
Homework Equations
The Attempt at a Solution
proving it for n=1
d^(1)x^1/dx = 1!=1 (a)
d/dx x^1 =1 (b)
a=b therefore at n=1 it is true
supposing it is true for n=k
then d^(k)x^k/dx = k!
verifying if it holds for n=k+1 and = (k+1)!
d^(k+1)x^(k+1)/dx = d/dx (d^(k)x^(k+1)/dx)
=d/dx(d^k/dx [x^k*x])=d/dx ([d^k/dx x^k * x]+[x^k d^k/dx x])
=d/dx ([k! * x]+[x^k * 0]
=d/dx x*k!=k!
this doesn't equal (k+1)! ,why?