Homework Help: Calculus 1

Posted by Alex on Monday, October 22, 2012 at 8:33pm.

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

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?

Calculus 1 - Steve, Tuesday, October 23, 2012 at 12:03am
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

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