Question

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

Answer 1

Use the chain rule:

$\dfrac{\mathrm dy}{\mathrm dx}=\dfrac{\mathrm dy}{\mathrm du}\dfrac{\mathrm du}{\mathrm dx}$

We have

$y=8u-6\implies\dfrac{\mathrm dy}{\mathrm du}=8$

$u=3x-8\implies\dfrac{\mathrm du}{\mathrm dx}=3$

so we get

$\dfrac{\mathrm dy}{\mathrm dx}=8\cdot3=\boxed{24}$

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

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