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

ka1leE

Answered question

2021-01-02

w=xsiny, x=et, y=πt, value t=0, find dwdt using the appropriate Chain Rule and evaluate dwdt at the given value of t.

Answer & Explanation

curwyrm

curwyrm

Skilled2021-01-03Added 87 answers

If w=xsiny, x=et, y=πt 
dwdt=dwdxdxdt+dwdydydt 
dwdt=ddx[xsiny]ddt[et]+ddy[xsiny]ddt[πt] 
dwdt=siny(et)+(xcosy)(1) 
dwdt=etsinyxcosy 
x=et, y=πt, so 
dwdt=etsin(πt)etcos(πt) 
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 

 

Answer
et(sint+cost), 1

Do you have a similar question?

Recalculate according to your conditions!

Ask your question.
Get an expert answer.

Let our experts help you. Answer in as fast as 15 minutes.

Didn't find what you were looking for?