Find the derivative of y with respect to x. y=(x^6/6)(lnx)-(x^6/36)

Question

So far this is what I've gotten:

y=(x^6/6)(lnx)-(x^6/36)
y=(1/6)x^6(lnx)-(1/36)x^6
y'=(1/6)x^5(1/x)+lnx(x^5)-(1/6)x^5

What do I do now?

Answer 1

You forgot various parts.

If y = uv, y' = u'v + uv'
If y = u^n, y' = nu^(n-1) u'

So,

y' = [1/6 * 6x^5 * lnx] + [1/6 x^6 * 1/x] - 1/36 * 6x^5

or, you can factor stuff out first:

y = 1/6 x^6 (lnx - 1/6)
y' = [1/6 * 6x^5](lnx - 1/6) + 1/6 x^6 * (1/x)

Either way you can massage things till you get

x^5 lnx