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Thread: More Differentiation Questions

  1. #1
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    More Differentiation Questions

    Hi
    A couple of problems i am having trouble with:

    1)$\displaystyle 3\sqrt{x}(x^2+2x)$
    2)Show that $\displaystyle \frac{d}{dx}(\sqrt{x^2+-a^2})=\frac{x}{\sqrt{x^2+-a^2}}$

    P.S
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  2. #2
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    Quote Originally Posted by Paymemoney View Post
    1)$\displaystyle 3\sqrt{x}(x^2+2x)$

    The product rule says

    For $\displaystyle y=u\times v \Rightarrow y' = u'\times v+u\times v'$

    In your case make $\displaystyle u = 3\sqrt{x} $ and $\displaystyle v = x^2+2x$

    Now find $\displaystyle u' $ and $\displaystyle v'$
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  3. #3
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    Quote Originally Posted by Paymemoney View Post
    Hi
    A couple of problems i am having trouble with:

    2)Show that $\displaystyle \frac{d}{dx}(\sqrt{x^2+-a^2})=\frac{x}{\sqrt{x^2+-a^2}}$

    P.S
    $\displaystyle \frac{d}{dx}{f(g(x))}=f'(g(x)) \times g'(x)$

    in this case, let $\displaystyle f(x)=\sqrt{x}$ and $\displaystyle g(x)=x^2+-a^2$
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  4. #4
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    Quote Originally Posted by pickslides View Post
    The product rule says

    For $\displaystyle y=u\times v \Rightarrow y' = u'\times v+u\times v'$

    In your case make $\displaystyle u = 3\sqrt{x} $ and $\displaystyle v = x^2+2x$

    Now find $\displaystyle u' $ and $\displaystyle v'$
    thanks got the right answer
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  5. #5
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    Quote Originally Posted by dedust View Post
    $\displaystyle \frac{d}{dx}{f(g(x))}=f'(g(x)) \times g'(x)$

    in this case, let $\displaystyle f(x)=\sqrt{x}$ and $\displaystyle g(x)=x^2+-a^2$
    i can't seen to get it correct.
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  6. #6
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    $\displaystyle f'(x)=\frac{1}{2\sqrt{x}}$
    $\displaystyle g'(x)=2x$

    then
    $\displaystyle f'(g(x)) \times g'(x) = . . . $
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  7. #7
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    isn't $\displaystyle g'(x) = 2x +- 2a$

    This is how i approached it:
    $\displaystyle =\frac{1}{2\sqrt(x^2)(2x)}$
    $\displaystyle =\frac{1}{2\sqrt{2x^3}}$

    This is where i get stuck i i don't know what can be done.
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  8. #8
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    a is a constant, it doesn't depend on $\displaystyle x$, so the derivative is $\displaystyle 0$.
    now you should be able to calculate $\displaystyle f'(g(x)) \times g'(x)$
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  9. #9
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    oh ok yeh i get it now
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