find the second derivative of x^n when n is greater than or equal to 2

Question

anonymous · Answer

power rule

anonymous · Answer

but what is throwing me off is the greater than sign

anonymous · Answer

just redundant information

anonymous · Answer

if x=1,then second or higher derivatives=0

geerky42 · Answer

You mean n=1?

campbell_st · Answer

start with this 

if you were given 

$$y = x^n$$

what would you write for the 1st derivative...?

anonymous · Answer

nx^(n-1)

campbell_st · Answer

great

and n is just a constant

so now what is the 2nd derivative...?

campbell_st · Answer

of just differentiate you last answer

campbell_st · Answer

so just apply the same method to find the 2nd derivative... 

$$y'= x^{n - 1}$$

then multiply the answer by n

anonymous · Answer

wouldn't it just be (n-1)(n-2)x^(n-2)

geerky42 · Answer

$$x^n\~\~\\dfrac{d}{dx}x^n = nx^{n-1}$$Let $m = n-1$

So we have $\dfrac{d}{dx}x^n  = nx^{n-1}=nx^{m}$


Now taking derivative again:
$\dfrac{d}{dx}n~x^m = n~m~x^{m-1} = n(n-1)x^{(n-1)-1} = \boxed{n(n-1)x^{n-2}}$