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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- Jan 15th 2008, 03:22 PMdumplingsDifferentiation
How would you differentiate y = (302x^2)(x^4 = x) ?

y = x^2 / 3x - 1?

Thank you fo any help assistance! - Jan 15th 2008, 03:32 PMJhevon
i suppose for the first problem you meant $\displaystyle y = 302x^2 \left( x^4 + x \right)$ ?

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

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

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

can you continue? - Jan 15th 2008, 04:30 PMKrizalid
I was lookin' for another way to tackle this. (Since I don't like quotient rule.)

$\displaystyle y = \frac{{x^2 }}

{{3x - 1}} = \frac{{(3x - 1)(3x + 1) + 1}}

{{9(3x - 1)}} = \frac{1}

{3}x + \frac{1}

{9} + \frac{1}

{{9(3x - 1)}}.$

Now from here is easy to contemplate its derivative.

$\displaystyle y' = \frac{1}

{3} - \frac{1}

{{3(3x - 1)^2 }}.$

And we're done. - Jan 15th 2008, 04:43 PMJhevon