1. Limited time only! Sign up for a free 30min personal tutor trial with Chegg Tutors
    Dismiss Notice
Dismiss Notice
Join Physics Forums Today!
The friendliest, high quality science and math community on the planet! Everyone who loves science is here!

Homework Help: Derivative of sin^2

  1. Jul 21, 2011 #1
    1. The problem statement, all variables and given/known data
    Derivative of Sin22x

    2. Relevant equations
    dy/dx = dy/du * du/dx


    3. The attempt at a solution
    Just want to make sure I am doing this right*.

    Do I let U = Sin2x or U = 2x?

    Let's say U = Sin2x

    then y` = 2Sin2x * cos2x?

    Or if U = 2x.

    y = SinU2

    y` = 2cos2x * 2
    y` = 4cos2x

    am i on the right track with either of these? any help is appreciated! thanks!
    Last edited by a moderator: Feb 14, 2013
  2. jcsd
  3. Jul 21, 2011 #2


    User Avatar
    Homework Helper

    Re: Derivative of Sin^2(2x)?

    You are halfway on the right track :smile:.

    Sin^2(2x)=F(U(V)): V=2x, U=sin(V), F=U^2.


  4. Jul 21, 2011 #3


    User Avatar
    Science Advisor

    Re: Derivative of Sin^2(2x)?

    You first let U= sin 2x so that [itex]y= U^2[/itex], [itex]y'= 2U U'[/itex].

    Then, to find U', let V= 2x so U= sin V. U'= cos(V)(V') and, of course, V'= 2.
    Put those together.

    No, because the derivative of sin2X is not cos2X. Use the chain rule again.

    No, because the derivative of [itex]sin^2(x)[/itex] is not [itex]cos^2(x)[/itex]

  5. Jul 22, 2011 #4
    Re: Derivative of Sin^2(2x)?

    Essentially, what this entire question boils down to:
    We need two applications of the chain rule.
    The first one started well.

    Instead of
    y` = 2Sin2x * cos2x
    I recommend beginning Calculus students write.
    y` = 2Sin2x * ( Sin2x )'
    The left factor, 2 Sin(2x) is finished.
    Then to evaluate the derivative of Sin 2x, apply chain rule a second time, with v =2x

    General hint, way to think of chain rule:
    Take deriv. of the outside, leave the inside alone , then multiply by deriv. of inside.
Share this great discussion with others via Reddit, Google+, Twitter, or Facebook