More on finding the nth derivative

[christen1289]

I have another question on finding the nth derivative. Is there a set formula i can follow for finding the nth derivative of different functions or do i need to find different patterns in order to come up with a formula each time.

I also need to find formulas for the nth derivative of:
f(x)= x^n

f(x)= 1/ (3x^3)

f(x)= square root of x

Does anyone know how these formulas or an easy way of coming up with them?

 

[genneth]

It's a guess. But for x^n it should be pretty easy -- a bit of induction should sort it out, and the other two are just a special cases.

 

[rock.freak667]

Only way I know how to get the nth derivative is to just differentiate about 3 times and hope to see a pattern

 

[dynamicsolo]

I have another question on finding the nth derivative. Is there a set formula i can follow for finding the nth derivative of different functions or do i need to find different patterns in order to come up with a formula each time.

I also need to find formulas for the nth derivative of:
f(x)= x^n

As genneth and rock.freak667 point out, the trickiest thing here is that there are different cases to consider. Try different starting values for n (remember, n can be any real number) and see what happens...

f(x)= 1/ (3x^3)

f(x)= square root of x

As with your other thread, it will make things easier if you start from

(3x^3)^(-1) and x^(1/2) .

 

[rock.freak667]

for the nth derivative of $$x^n$$ try differentiating that about 4 times and try to deduce the 5th derivative














(hint: n(n-1)(n-2)(n-3)(n-4)(...)=n!)