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Math Help - Differentiate Question

  1. #1
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    Differentiate Question

    Question:
    Differentiate with respect to x:

    y = \frac{x + 3}{x - 2}

    Any help is thanked.
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  2. #2
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    I assume you learnt some differentiation.

    Use the quotient rule:

    when y = u/v

    dy/dx = [v(du/dx) - u (dv/dx)] / v

    In your case y= (x+3)/(x-2) so

    dy/dx = [(x-2)1 - (x+3)1] / (x-2)

    = (x-2-x-3)/ (x-2)
    = -5 / (x-2)

    I like to keep it in brackets, but you can expand if needed.
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  3. #3
    Math Engineering Student
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    Quote Originally Posted by name101 View Post
    Question:
    Differentiate with respect to x:

    y = \frac{x + 3}{x - 2}

    Any help is thanked.
     <br />
\begin{aligned}<br />
y &= \frac{{x + 3}}<br />
{{x - 2}}\\<br />
&= \frac{{x - 2 + 5}}<br />
{{x - 2}}\\<br />
&= 1 + 5\left( {x - 2} \right)^{ - 1}\\<br />
y' &= - \frac{5}<br />
{{\left( {x - 2} \right)^2 }}<br />
\end{aligned}<br />
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