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Math Help - respect to x

  1. #1
    marikas
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    respect to x


    2. Differentiate the following functions with respect to
    x:
    (a)
    y = 3x^4

    (b)
    y = 3 sin(2x)

    Hint: Use the chain–rule with
    u = 2x.

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  2. #2
    MHF Contributor
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    Quote Originally Posted by marikas View Post

    2. Differentiate the following functions with respect to
    x:
    (a) y = 3x^4
    (b)


    y = 3 sin(2x)
    Hint: Use the chain–rule with


    u = 2x.
    You have a hint. Why not use it.

    a) 12x^3
    b) 6cos(2x)

    You REALLY can't do these? You may need to have a serious chat with your academic advisor.

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  3. #3
    Math Engineering Student
    Krizalid's Avatar
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    C'mon TKHunny, remember that some people are not as smart as you.

    Quote Originally Posted by marikas View Post

    2. Differentiate the following functions with respect to
    x:

    (a) y = 3x^4
    (b)


    y = 3 sin(2x)

    Hint: Use the chain–rule with


    u = 2x.
    For letter a), you need to know that (x^n)'=nx^{n-1}, for n a rational number.

    For letter b), I'll use two ways:

    y'=3\cos(2x)\cdot(2x)'=3\cos(2x)\cdot2=6\cos2x.

    --

    Define u=2x\implies u'=2. Since y=3\sin u\implies y'=3\cos u\cdot u'.

    Now back substitute

    y'=3\cos2x\cdot2=6\cos2x.

    Hope it helps
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