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Math Help - derivatives involving square roots

  1. #1
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    derivatives involving square roots

    Find f '(a).

    f(x) = √5x + 1



    I Know i can turn it into (5x+1)^.5 but im lost from here on out.
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  2. #2
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    Quote Originally Posted by Evan.Kimia View Post
    Find f '(a).

    f(x) = √5x + 1



    I Know i can turn it into (5x+1)^.5 but im lost from here on out.
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    is it  f(x)=\sqrt {5x}+1 \quad or \quad f(x)=\sqrt {5} {x}+1 ?
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  3. #3
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    the square root covers that whole function.
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  4. #4
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     f(x)=\sqrt{(5x+1)}

    use chain rule

     f'(x)=\frac{d}{dx}f(x)=\frac{d{f(x)}}{dt} \cdot \frac{dt}{dx}

    assume t=5 x+1
    so that f(x)=  t^{\frac{1}{2}}

    if stuck see spoiler
    Spoiler:

     \frac{d{f(x)}}{dt} = \frac{1}{2} t^{\frac{-1}{2}}=\frac{1}{2 \sqrt {t}}=\frac{1}{2 \sqrt {5 x+1    }}
     \frac{dt}{dx}=\frac{d{(5 x+1) }}{dx}=5
     f'(x)=\frac{d{f(x)}}{dt} \cdot \frac{dt}{dx} =\frac{1}{2 \sqrt {5 x+1    }} \cdot 5=\frac{5}{2 \sqrt {5 x+1    }}
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