Question

Find dy/dx. if y = 8u - 6 and u = 3x - 8.

dy/dx =
Can someone please explain how I would solve this calculus problem? Thanks!

Answer 1

Use the chain rule:

`(\mathrm dy)/(\mathrm dx)=(\mathrm dy)/(\mathrm du)(\mathrm du)/(\mathrm dx)`

We have

`y=8u-6\implies(\mathrm dy)/(\mathrm du)=8`

`u=3x-8\implies(\mathrm du)/(\mathrm dx)=3`

so we get

`(\mathrm dy)/(\mathrm dx)=8\cdot3=\boxed{24}`

Alternatively, you can substitute u in the definition of y and differentiate with respect to x :

`y=8u-6=8(3x-8)=24x-64\implies(\mathrm dy)/(\mathrm dx)=24`