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!

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1. Use the chain rule:

   [tex]\dfrac{\mathrm dy}{\mathrm dx}=\dfrac{\mathrm dy}{\mathrm du}\dfrac{\mathrm du}{\mathrm dx}[/tex]

   We have

   [tex]y=8u-6\implies\dfrac{\mathrm dy}{\mathrm du}=8[/tex]

   [tex]u=3x-8\implies\dfrac{\mathrm du}{\mathrm dx}=3[/tex]

   so we get

   [tex]\dfrac{\mathrm dy}{\mathrm dx}=8\cdot3=\boxed{24}[/tex]

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

   [tex]y=8u-6=8(3x-8)=24x-64\implies\dfrac{\mathrm dy}{\mathrm dx}=24[/tex]

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