If y= Find dy/dx

Question

y= (4x-5)^3 (4x+2)^3 find dy/dx

how do i solve this problem to find dy/dx?

Answer 1

Answer 2

There are 2 ways to approach this problem...both messy!

This problem is not necessarily instructive, but I will try to help a little.

First you can expand both binomials and multiply the resulting products together to get a 6th degree polynomial and the differentiate term by term.

Or you can use the product rule without expanding the binomials and use the chain rule with the derivatives.

I warned you...both are messy solutions!

Answer 3

You use the product rule for differentiation:

If y = f(x) * g(x)

y' = f(x)*g'(x) + f'(x)*g(x)

The pieces:

f(x) = (4x - 5)³, so

f'(x) = 3(4x - 5)² * 4 = 12(4x - 5)²

g(x) = (4x + 2)³, so

g'(x) = 3(4x + 2)² * 4 = 12(4x + 2)²

Plug all this into the formula and simplify.....