How would you differentiate the following ?
y=(2x^2-1)(4x^3+x)
and
y= (x+5) / (3x^2 -6x)
Here, apply the product rule: for differentiable functions $\displaystyle f$ and $\displaystyle g$, we define the derivative of their product as follows:
$\displaystyle (f \cdot g)' = f' \cdot g + f \cdot g'$
now try it
apply the quotient rule: for differentiable functions $\displaystyle f$ and $\displaystyle g$ we define the derivative of their ratio as follows:y= (x+5) / (3x^2 -6x)
$\displaystyle \left( \frac fg \right)' = \frac {f'g - fg'}{g^2}$
now try it