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Math Help - Derivative Question?

  1. #1
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    Derivative Question?

    Hi All!

    I am new to this topic and not sure if it is correct place to post this.

    I know simple derivative like x^3-x-1. For x^3 we multiply it by power and subtract 1 from power which is equal to 3x^2, x will become 1 and derivative of 1 is 0 so answer is

    3x^2-1

    Don't know how to calculate derivative of
    Derivative Question?-math.gif
    Any help please?

    Another thing, where to download Latex.pdf? this link doesn't work.

    Thanks in advance
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  2. #2
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    Quote Originally Posted by mrsenim View Post
    Hi All!

    I am new to this topic and not sure if it is correct place to post this.

    I know simple derivative like x^3-x-1. For x^3 we multiply it by power and subtract 1 from power which is equal to 3x^2, x will become 1 and derivative of 1 is 0 so answer is

    3x^2-1

    Don't know how to calculate derivative of
    y = \frac{1}{\sqrt{x+1}}
    Any help please?

    Another thing, where to download Latex.pdf? this link doesn't work.

    Thanks in advance
    Chain rule works best here IMO.

    Let u = x+1. This should be pretty easy to solve for \frac{du}{dx}

    Thus we get y = \frac{1}{\sqrt{u}}.

    Remembering the laws of exponents this is equal to y = u^{-1/2} which differentiates in the same way as the positive integers so you can find \frac{dy}{du}.

    Here's where the chain rule comes in:

    \frac{dy}{dx} = \frac{dy}{du} \times \frac{du}{dx}

    You should have and expression for both those terms
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  3. #3
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    \frac{1}{\sqrt{x + 1}} = (x + 1)^{-\frac{1}{2}}.

    Now you need to use the Chain Rule.
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  4. #4
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    Quote Originally Posted by Prove It View Post
    \frac{1}{\sqrt{x + 1}} = (x + 1)^{-\frac{1}{2}}.

    Now you need to use the Chain Rule.
    I tried to solve it as follows

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

    Now multiplying by -1/2 and subtracting 1 from power

    = {-\frac{1}{2}}[(x + 1)^{-\frac{3}{2}}]

    = {-\frac{1}{2}}[\frac{1}{(x + 1)^{\frac{3}{2}}}]

    Is it correct?

    Where to download latex.pdf? Thanks!

    Don't know what is chain rule.
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  5. #5
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    Quote Originally Posted by mrsenim View Post
    I tried to solve it as follows

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

    Now multiplying by -1/2 and subtracting 1 from power

    = {-\frac{1}{2}}[(x + 1)^{-\frac{3}{2}}]

    = {-\frac{1}{2}}[\frac{1}{(x + 1)^{\frac{3}{2}}}]

    Is it correct?

    Where to download latex.pdf? Thanks!

    Don't know what is chain rule.
    In that case you managed to use the chain rule without knowing because your answer is correct

    The reason is because in this case you only needed to multiply by the derivative of (x+1) which is 1
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