Question

Use the chain rule to find ∂z∂s and ∂z∂t, where z=x2+xy+y2,x=10s+7t,y=10s+3t

Answer 1

`(\partial z)/(\partial s)=(\partial z)/(\partial x)(\partial x)/(\partial s)+(\partial z)/(\partial y)(\partial y)/(\partial s)`

`(\partial z)/(\partial s)=(2x+y)(10)+(x+2y)(10)=30x+30y`

`(\partial z)/(\partial s)=30(10s+7t)+30(10s+3t)=600s+300t`


`(\partial z)/(\partial t)=(\partial z)/(\partial x)(\partial x)/(\partial t)+(\partial z)/(\partial y)(\partial y)/(\partial t)`

`(\partial z)/(\partial t)=(2x+y)(7)+(x+2y)(3)=17x+13y`

`(\partial z)/(\partial t)=17(10s+7t)+13(10s+3t)=300s+158t`