Find dw/dt using the appropriate Chain Rule. Evaluate frac{dw}{dt} at the given value of t. Function: w=xsin y, x=e^t, y=pi-t Value: t = 0

ka1leE 2021-01-02 Answered

Find dwdt using the appropriate Chain Rule. Evaluate dwdt at the given value of t. Function: w=xsiny, x=et, y=πt Value: t=0

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Expert Answer

curwyrm
Answered 2021-01-03 Author has 87 answers
Let w=xsiny, x=et, y=πt
Apply the chain Rule for One independet Variable
dwdt=dwdxdxdt+dwdydydt
So
dwdt=ddx[xsiny]ddt[et]+ddy[xsiny]ddt[πt]
Calculate the Partial derivatives, you get
dwdt=siny(et)+(xcosy)(1)
Simplify
dwdt=etsinyxcosy
Substitute x=et, y=πt, so
dwdt=etsin(πt)etcos(πt)
Remember that sin(πt)=sint and cos(πt)=cost, so
dwdt=etsintet(cost)
dwdt=et(sint+cost)
Evaluate dwdt when t =0
dwdt=e0(sin0+cos0)
dwdt=1(0+1)
dwdt=1
Results
et(sint+cost), 1
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