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Math Help - differentiation questions

  1. #1
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    Question differentiation questions??? :(

    HELP PLEASE! there's a time limit to this. it's homework, not a quiz. but i have tried and tried. i'm dead serious.

    can you guys help?

    Differentiate the following function.
    would i foil and then differentiate? because i've tried that over and over.

    and then another:

    Differentiate.
    (honestly, i don't understand why i can't get THAT one..i get the same answer over and over.... ((32/3)t^1/3) - ((5/6)t^-1/6)...errggggg

    i'm sorry. i'm not usually a questions person. but i am highly interested in calculus. please help??
    Last edited by jayjay60; September 27th 2009 at 03:06 PM.
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  2. #2
    Senior Member DeMath's Avatar
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    Quote Originally Posted by jayjay60 View Post
    i have tried and tried. i'm dead serious.

    can you guys help?

    Differentiate the following function.
    would i foil and then differentiate? because i've tried that over and over.

    and then another:

    Differentiate.
    (honestly, i don't understand why i can't get THAT one..i get the same answer over and over.... ((32/3)t^1/3) - ((5/6)t^-1/6)...errggggg

    i'm sorry. i'm not usually a questions person. but i am highly interested in calculus.
    For 1

    u = {\left( {5\sqrt x  + \frac{6}<br />
{{5\sqrt[3]{x}}}} \right)^2} \Rightarrow \frac{{du}}<br />
{{dx}} = \frac{d}<br />
{{dx}}{\left( {5\sqrt x  + \frac{6}<br />
{{5\sqrt[3]{x}}}} \right)^2} =

    = 2\left( {5\sqrt x  + \frac{6}<br />
{{5\sqrt[3]{x}}}} \right) \cdot \frac{d}<br />
{{dx}}\left( {5\sqrt x  + \frac{6}<br />
{{5\sqrt[3]{x}}}} \right) =

    = 2\left( {5\sqrt x  + \frac{6}<br />
{{5\sqrt[3]{x}}}} \right)\left[ {\frac{d}<br />
{{dx}}\left( {5\sqrt x } \right) + \frac{d}<br />
{{dx}}\left( {\frac{6}<br />
{{5\sqrt[3]{x}}}} \right)} \right] =

    = 2\left( {5\sqrt x  + \frac{6}<br />
{{5\sqrt[3]{x}}}} \right)\left( {\frac{5}<br />
{{2\sqrt x }} - \frac{2}<br />
{{5\sqrt[3]{{{x^4}}}}}} \right) =

    = 25 - \frac{4}<br />
{{\sqrt[6]{{{x^5}}}}} + \frac{6}<br />
{{\sqrt[6]{{{x^5}}}}} - \frac{{24}}<br />
{{25\sqrt[3]{{{x^5}}}}} =

    = 25 + \frac{2}<br />
{{\sqrt[6]{{{x^5}}}}} - \frac{{24}}<br />
{{25\sqrt[3]{{{x^5}}}}}.
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  3. #3
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    oh wow!

    this question was in my sctn 3.3 hwk.
    we learned THAT formula in 3.4.

    oh man, i was so confused.
    but seriously.

    i honestly praise you. you're my favorite person ever atm. <3
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  4. #4
    Senior Member DeMath's Avatar
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    Quote Originally Posted by jayjay60 View Post
    HELP PLEASE! there's a time limit to this. it's homework, not a quiz. but i have tried and tried. i'm dead serious.

    can you guys help?

    Differentiate the following function.
    would i foil and then differentiate? because i've tried that over and over.

    and then another:

    Differentiate.
    (honestly, i don't understand why i can't get THAT one..i get the same answer over and over.... ((32/3)t^1/3) - ((5/6)t^-1/6)...errggggg

    i'm sorry. i'm not usually a questions person. but i am highly interested in calculus. please help??
    For 2

    g\left( t \right) = \frac{{8t - \sqrt t }}<br />
{{{t^{1/3}}}} = 8{t^{2/3}} - {t^{1/6}} \Rightarrow

    \Rightarrow \frac{d}<br />
{{dx}}g\left( t \right) = \frac{d}<br />
{{dx}}\left( {8{t^{2/3}} - {t^{1/6}}} \right) =

    = \frac{{16}}<br />
{3}{t^{ - 1/3}} - \frac{1}<br />
{6}{t^{ - 5/6}} = \frac{{16}}<br />
{{3{t^{1/3}}}} - \frac{1}<br />
{{6{t^{5/6}}}}.
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