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Math Help - differentiation

  1. #1
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    differentiation

    not sure how todo differentiations
    can any one explain how to do this equasion

    y=3x^4 -3√x+8
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  2. #2
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    Quote Originally Posted by bart 1000 View Post
    not sure how todo differentiations
    can any one explain how to do this equasion

    y=3x^4 -3√x+8
    y = 3x^4 - 3x^{1/2} + 8

    \frac{dy}{dx} = 12x^3 - 1.5x^{-1/2}
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  3. #3
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    Quote Originally Posted by bart 1000 View Post
    not sure how todo differentiations
    can any one explain how to do this equasion

    y=3x^4 -3√x+8
    First lets quote the power rule

    \frac{d}{dx}x^n=nx^{n-1}

    Now lets rewrite y with fractional exponents using

    \sqrt[b]{x^a}=x^{\frac{a}{b}}

    So

    y=3x^4-3x^{\frac{1}{2}}+8

    Just use the power rule
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  4. #4
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    thanks for your help, i understand how to get 12x^3 but getting a bit lost on
    what happens to -3√x+8 ??????
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  5. #5
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    Quote Originally Posted by bart 1000 View Post
    thanks for your help, i understand how to get 12x^3 but getting a bit lost on
    what happens to -3√x+8 ??????
    √x = x^0.5

    So, lower the power by 1 to make it -1/2, then multiply the co-efficient by 1/2 to make it -1.5
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  6. #6
    Behold, the power of SARDINES!
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    Quote Originally Posted by bart 1000 View Post
    thanks for your help, i understand how to get 12x^3 but getting a bit lost on
    what happens to -3√x+8 ??????

    Do you mean?

    \sqrt{x+8}=(x+8)^{\frac{1}{2}}

    If so

    \frac{d}{dx}(x+8)^{\frac{1}{2}}=\frac{1}{2}(x+8)^{-\frac{1}{2}}=\frac{1}{2\sqrt{x+8}}
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