Calculus

Could someone please check my work on the following problems? I want to be sure that I'm doing them correctly; i'm just required to find the derivatives and then simplify.


g(t)= t/sint
g'(t)=1*sint-cost*t/(sint)^2
g'(t)=sint-cost*t/(sint)^2

y=ln(e^ax)
y'=1/e^ax*e^x*a

and i'm sort of stuck on this one
y=e^2x[sin(3x)^2]^2
Y'=2^ex*sin(3X)^2+e^2x[2cos3x]
i got this far, but i'm not sure how to simplify that.

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asked by Joesph
  1. my version:
    g(t)= t/sint
    g'(t) = (sin t -t cos t)/sin^2t
    your version:
    g'(t)=1*sint-cost*t/(sint)^2
    g'(t)=sint-cost*t/(sint)^2

    y=ln(e^ax)

    my version:
    y = a x ln (e) = a x
    y' = a

    your version:
    y'=1/e^ax*e^x*a times a because d/dx(e^ax) = a e^ax

    but that is just x a

    and i'm sort of stuck on this one
    y=e^2x[sin(3x)^2]^2

    my version:
    [sin(3x)^2]^2 * 2 e^2x + e^2x * 2 [sin(3x)^2]^1 * d/dx(sin(3x)^2)

    = 2 e^2x *{[sin(3x)^2]^2 + sin(3x)^2 * sin(3x)^2* [cos(3x)^2] *2*3x*3]

    = 2 e^2x * sin(3x)^2]^2 *{ 1 + 18xcos(3x)^2}
    wow - check my arithmetic

    Your version:

    Y'=2^ex*sin(3X)^2+e^2x[2cos3x]

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    posted by Damon

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