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

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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Delwyn 1 year 2021-08-11T14:14:07+00:00 1 Answers 0 views 0

Answers ( )

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    2021-08-11T14:15:39+00:00

    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

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