Use the Chain Rule to find dz / ds and dz / dt. z=(x-y)5, x=s^2t, y=st^2Z

Dottie Parra

Dottie Parra

Answered question

2021-10-24

Use the Chain Rule to find dz / ds and dz / dt.
z=(xy)5,x=s2t,y=st2

Answer & Explanation

Adnaan Franks

Adnaan Franks

Skilled2021-10-25Added 92 answers

Finding dzdt and finding dzds
We can write
dzds=dzdt=dzdxdxds+dzdydyds
Let us fint the necessary partial derivates
dzdx=d[(xy)5]dx=5(xy)4
dzdy=d[(xy)5]dy=5(xy)4
dxds=d[s2t]ds=2st
dyds=d[st2]ds=t2
Substitute the expressions
dzds=5(xy)42st5(xy)4t2
dzds=5(xy)4(2stt2)
Result: dzds=dzdt=5(xy)4(2stt2)

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