I was wondering if someone could show me how to do this?
Differentiate Value of
I can't figure it out
If you mean "differentiate both sides of this equation with respect to a", then, since the right side is a constant with respect to a, and using the product rule and chain rule, .
If neither of those is what you mean, then I have no idea what you do mean.
Vince has simply left the numerator "written" as a cube,
since you can now apply the chain rule to it,
or simply multiply out
Was it your idea to substitute
in the beginning?
Or was that requested by the question?
You see, you can do things the short way using x,
then manipulating the fraction to a simpler manageable one as Vince did.
Or... use the messy substitution and get some good experience with the Chain Rule.
Let me know the drive of the question,
I can show you the way using the substitution if you want to play along with it.
Since you have a product after your substitution,
you need to use a combination of product and chain rule.
It's much faster to do it the way Vince showed.
Nevertheless, here's what to do with the "a" substitution...
Putting all these together
We can write all of these terms using x to get the answer you are seeking.
Therefore the derivative is