Calculus 1
posted by Alex on .
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?

You forgot various parts.
If y = uv, y' = u'v + uv'
If y = u^n, y' = nu^(n1) 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