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Math Help - differentitation help please !!!!

  1. #1
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    differentitation help please !!!!

    could anyone help me with these questions please i have a few answers myslef but dont know if i am going the right way with this or not. im useless at differentiation please be kind lol !!!

    Q1, differentiate the following with respect to X


    a, Y=squareroot of(x^3+5)


    p.s dnt know how to get square root sign on p.c



    b, Y=X^3sin2x




    c, Y=e^2x /(x+3)




    thankyou for your time hopefully some of you are better at this than me lol im sure you are !!!!!
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  2. #2
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    We can't say if you are "going the right way" if you don't show us which way you are going! Show what you are doing, please.
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  3. #3
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    a) let  u = x^{3} + 5 and use the chain rule


    b) product rule

    \sin(2x) \frac{d}{dx} x^{3} + x^{3} \frac {d}{dx} \sin(2x)


    c) quotient rule

     \frac{(x+3)\frac{d}{dx}e^{2x} - e^{2x}\frac {d}{dx} (x+3)}{(x+3)^2}
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  4. #4
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    Quote Originally Posted by lukyleo26 View Post
    could anyone help me with these questions please i have a few answers myslef but dont know if i am going the right way with this or not. im useless at differentiation please be kind lol !!!

    Q1, differentiate the following with respect to X


    a, Y=squareroot of(x^3+5)
    y = \sqrt{x^3+5} = (x^3+5)^{\frac{1}{2}}. You can then use the chain rule to solve

    Spoiler:
    y' = \frac{3}{2} \cdot \frac{x^2}{\sqrt{x^3+5}}



    b, Y=X^3sin2x
    Product Rule: y=f(x)g(x) \: , \: y' = f'(x)g(x) + g'(x)f(x)

    In your case f(x) = x^3 and g(x) = sin(2x). Note that you must use the chain rule on sin(2x).

    Spoiler:
    u = x^3 \: , \: v = sin(2x)
    u' = 3x^2 \: , \: v' = 2cos(2x)

    y' = 2x^3cos(2x) + 3x^2sin(2x)



    c, Y=e^2x /(x+3)
    Quotient Rule: y = \frac{u}{v} \: , \: y' = \frac{vu' - uv'}{v^2}

    In your case u = e^{2x} (and don't forget the chain rule) and v = x+3

    Spoiler:
    u = e^{2x} \: , \: v = x+3
    u' = 2e^{2x} \: , \: v' = 1

    y' = \frac{2(x+3)e^{2x} - e^{2x}}{(x+3)^2} = \frac{e^{2x}(2x+5)}{(x+3)^2}
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  5. #5
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    for b is the answer


    yx^3*sin2*X

    Fx=sin2*yx^3

    f/x= sin2yx^3
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