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Math Help - Derivative help

  1. #1
    Junior Member
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    Derivative help

    I need to find the derivative of the function:

    f(x)= x + 1 / \sqrt{x}


    / = divided by


    Can someone show me step by step how I'd go about solving down? And if possible guide me on the steps they've used? Thanks!
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  2. #2
    Member Nacho's Avatar
    Joined
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    Santiago, Chile
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    <br />
\frac{d}<br />
{{dx}}\left( {x + \frac{1}<br />
{{\sqrt x }}} \right) = \frac{d}<br />
{{dx}}\left( {x + x^{ - 1/2} } \right)\underbrace  = _{{\text{sum rule}}}\frac{d}<br />
{{dx}}\left( x \right) + \frac{d}<br />
{{dx}}\left( {x^{ - 1/2} } \right)<br />

    But <br />
\frac{d}<br />
{{dx}}x^q  = q \cdot x^{q - 1} ,{\text{ }}\forall q \in \mathbb{Q}<br />

    Therefore: <br />
\frac{d}<br />
{{dx}}\left( x \right) + \frac{d}<br />
{{dx}}\left( {x^{ - 1/2} } \right) = 1 \cdot x^0  + \frac{{ - 1}}<br />
{2} \cdot x^{\frac{{ - 1}}<br />
{2} - 1}  = 1 + \frac{{ - 1}}<br />
{2} \cdot x^{ - 3/2}  = 1 + \frac{1}<br />
{{\sqrt {x^3 } }}<br />
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