f(x) = (1+x+x^2)^n find the second derivative

Question

phoenixfire · Answer

with respect to? x or n?

anonymous · Answer

x

lgbasallote · Answer

chain rule

lgbasallote · Answer

use power rule on (1 + x + x^2)^n then take the derivative of (1 + x + x^2)

lgbasallote · Answer

then multiply those

phoenixfire · Answer

Chain Rule: $${d \over dx}(f(g)) = f^{\prime}(g)g^{\prime}$$
so, take your equation and assign new functions.
$$f= outer function = x^n$$
$$g=inner function=x^2+x+1$$
find the derivative of f and g, then plug into chain rule.

Now you have first derivative.

phoenixfire · Answer

Once you get your result, post it so we can see if you're on the right track.

kainui · Answer

If you know how to take the first derivative, you almost definitely know how to take the second derivative. Just take the derivative twice, it's really that simple. Don't let the n confuse you, just keep doing what you always did, except when you when from an exponent of 3 to 2 you go from n to n-1. That's it, really.

phoenixfire · Answer

@hanzi 
first derivative is: $$n(2x+1)(x^2+x+1)^{n-1}$$