# Thread: Please help on derivatives

1. ## Please help on derivatives

This is the problem.
Find the first and second derivatives.
y=[(x^(2)-7)/56x][(x^(4)+1)/x^3]

So do I multiply across first or use quiotient rule for each of them?

2. Is this what it looks like? If so yes you can multiply them together and then use quotient rule.

$y= \bigg(\frac{x^2-7}{56x}\bigg)\bigg(\frac{x^4+1}{x^3}\bigg)$

Another way to do it is Logarithmic Differentiation

3. $y= \bigg(\frac{x^2-7}{56x}\bigg)\bigg(\frac{x^4+1}{x^3}\bigg)$

if we simplify it like this it will be easier i think

$
=\bigg(\frac{x^2}{56x}-\frac{7}{56x}\bigg) \bigg(\frac{x^4}{x^3}+\frac{1}{x^3}\bigg)
$

$=\bigg(\frac{x}{56}-\frac{1}{8x}\bigg) \bigg(x+\frac{1}{x^3}\bigg)$
$

= \bigg(\frac{x^2}{56}+\frac{1}{56x^2}-\frac{1}{8}-\frac{1}{8x^4}\bigg)
$

you can differentiate them one by one, factor out constants
and for the second derivative try to simplify the result of the first derivative as much as you can then start to differentiate it again.