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 $\displaystyle y = 302x^2 \left( x^4 + x \right)$ ?
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?
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.