# Differentiation

• January 15th 2008, 03:22 PM
dumplings
Differentiation
How would you differentiate y = (302x^2)(x^4 = x) ?
y = x^2 / 3x - 1?
Thank you fo any help assistance!
• January 15th 2008, 03:32 PM
Jhevon
Quote:

Originally Posted by dumplings
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?
• January 15th 2008, 04:30 PM
Krizalid
Quote:

Originally Posted by Jhevon
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.)

$y = \frac{{x^2 }}
{{3x - 1}} = \frac{{(3x - 1)(3x + 1) + 1}}
{{9(3x - 1)}} = \frac{1}
{3}x + \frac{1}
{9} + \frac{1}
{{9(3x - 1)}}.$

Now from here is easy to contemplate its derivative.

$y' = \frac{1}
{3} - \frac{1}
{{3(3x - 1)^2 }}.$

And we're done.
• January 15th 2008, 04:43 PM
Jhevon
Quote:

Originally Posted by Krizalid
I was lookin' for another way to tackle this. (Since I don't like quotient rule.)

$y = \frac{{x^2 }}
{{3x - 1}} = \frac{{(3x - 1)(3x + 1) + 1}}
{{9(3x - 1)}} = \frac{1}
{3}x + \frac{1}
{9} + \frac{1}
{{9(3x - 1)}}.$

Now from here is easy to contemplate its derivative.

$y' = \frac{1}
{3} - \frac{1}
{{3(3x - 1)^2 }}.$

And we're done.

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

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