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!

Question

asked Dec 14, 2021 130k views

1 Answer

Illidan · Answer 1 · 2021-12-20T19:18:19+0000

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 :

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