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Math Help - Differentiation

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    Differentiation

    How would you differentiate y = (302x^2)(x^4 = x) ?
    y = x^2 / 3x - 1?
    Thank you fo any help assistance!
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    is up to his old tricks again! Jhevon's Avatar
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    Quote Originally Posted by dumplings View Post
    How would you differentiate y = (302x^2)(x^4 = x) ?
    y = x^2 / 3x - 1?
    Thank you fo any help assistance!
    i suppose for the first problem you meant y = 302x^2 \left( x^4 + x \right) ?

    in that case, expand the brackets and then use the power rule: \frac d{dx} x^n = nx^{n - 1} (we could use the product rule, but i like this way more)

    for the second question i assume you meant y = \frac {x^2}{3x - 1} (use parentheses!)

    in that case, we would use the quotient rule: \left( \frac uv \right)' = \frac {vu' - uv'}{v^2}

    can you continue?
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  3. #3
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    Quote Originally Posted by Jhevon View Post
    for the second question i assume you meant y = \frac {x^2}{3x - 1} (use parentheses!)
    I was lookin' for another way to tackle this. (Since I don't like quotient rule.)

    y = \frac{{x^2 }}<br />
{{3x - 1}} = \frac{{(3x - 1)(3x + 1) + 1}}<br />
{{9(3x - 1)}} = \frac{1}<br />
{3}x + \frac{1}<br />
{9} + \frac{1}<br />
{{9(3x - 1)}}.

    Now from here is easy to contemplate its derivative.

    y' = \frac{1}<br />
{3} - \frac{1}<br />
{{3(3x - 1)^2 }}.

    And we're done.
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  4. #4
    is up to his old tricks again! Jhevon's Avatar
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    Quote Originally Posted by Krizalid View Post
    I was lookin' for another way to tackle this. (Since I don't like quotient rule.)

    y = \frac{{x^2 }}<br />
{{3x - 1}} = \frac{{(3x - 1)(3x + 1) + 1}}<br />
{{9(3x - 1)}} = \frac{1}<br />
{3}x + \frac{1}<br />
{9} + \frac{1}<br />
{{9(3x - 1)}}.

    Now from here is easy to contemplate its derivative.

    y' = \frac{1}<br />
{3} - \frac{1}<br />
{{3(3x - 1)^2 }}.

    And we're done.
    nice. of course we could have also used the product rule here if that suits your fancy

    just write as y = x^2 (3x - 1)^{-1}
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