Find dw/dt using the appropriate Chain Rule. Evaluate dw/dt at

Lucille Smitherman

Lucille Smitherman

Answered question

2021-11-13

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

Answer & Explanation

Steacensen69

Steacensen69

Beginner2021-11-14Added 15 answers

Let w=xsiny; x=et, y=πt
Apply the chain Rule for One indepedndent 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)
dw

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