Calculus 1

posted by .

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 -

    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

Respond to this Question

First Name
School Subject
Your Answer

Similar Questions

  1. calculus

    (a) find the intervals on which f is incrs or decrs. (b) find the local min/max values of f. (c) find the intervals of concavity and the inflection points. f(x)=(lnx)/sqrtx I took the derivative and got 2-lnx/2x^3/2 take the values …
  2. calc

    integral of 1 to e^4 dx/x(1+lnx) 1+lnx = a => dx/x = da dx/ x(1+lnx) = da/a int of da/a = In(a) =>int of dx/ x(1+lnx) = In(1+In(x)) + C from 1 to e^4 for int of dx/ x(1+lnx) = In(1+In(1)) - In(1+In(e^4)) In(1+In(1)) - In(1+In(e^4)) …
  3. Math

    Find the coordinates of the turning point and determine wether it is minimum or maximum. y=xlnx-2x The answer in the book says the co-ordinates are (e,-e), the closest I have come is (1/lnx,-1/lnx) which works if 1/lnx=e, but I don't …
  4. Calculus

    Find the derivative of y with respect to x. y= [(x^5)/5]lnx-[(x^5)/25] How would I go about doing this?
  5. L'Hopital's rule

    Find lim x->1+ of [(1/(x-1))-(1/lnx)]. Here is my work... =(lnx-(x-1)) / ((x-1)(lnx)) =(lnx-1) / (lnx+ (x+1)/x) This becomes(1/x) / ((1/x)+(1/x^2)) which becomes 1/ (1/x^2) This equals 1/2. I understand the answer has to be -1/2, …
  6. College Calc

    Problem: y=sqrtx ^1/x. Find DY/DX. ln(f(x))=lnx^1/2x or lnx to the 1/2x 1/2x lnx product rule (1/4x^2)(lnx)+(1/x)(1/2x) is the product rule correct?
  7. calculus

    sorry to ask a second question so soon, but i'm just not getting this one. if f(x)= 3x lnx, then f'(x)=?
  8. Calculus

    Find the derivatives, dy/dx for the following functions. a. x^2y^4 = lnx + 3y b. y = ln(2x^2 + 1) c. y = ln(ãx) d. y = lnx/x e. y = x^2 lnx f. y ß log_2⁡(3x)
  9. Calculus

    what is the limit as h approaches 0 of ((x+h)^pi-x^pi)/h?
  10. math: pre-calculus

    Let u=lnx and v=lny. Write the expression ln3√x/2y in terms of u and v. For example, lnx^3y=lnx^3+lny=3lnx +lny= 3u+v.

More Similar Questions