SOLUTION: Differentiate the following functions with respect to t: i) y = 2t^2. Cos(t) ii) y = Cos(t)/Sin(t) iii) y = e^pi t - e^-pi t Thanks!

Algebra ->  Polynomials-and-rational-expressions -> SOLUTION: Differentiate the following functions with respect to t: i) y = 2t^2. Cos(t) ii) y = Cos(t)/Sin(t) iii) y = e^pi t - e^-pi t Thanks!      Log On


   

Question 77908: Differentiate the following functions with respect to t:
i) y = 2t^2. Cos(t)
ii) y = Cos(t)/Sin(t)
iii) y = e^pi t - e^-pi t
Thanks!
Answer by Edwin McCravy(20060) About Me  (Show Source):
You can put this solution on YOUR website!

Differentiate the following functions with respect to t: 

i) y+=+2t%5E2%2Acos%28t%29 

   y+=+2%28t%5E2%2Acos%28t%29%29

   %28dy%29%2F%28dt%29+=+2%28+t%5E2%28+-sin%28t%29+%29+%2B+cos%28t%29%2A2t+%29+

   %28dy%29%2F%28dt%29+=+2%28-t%5E2%2Asin%28t%29++%2B+2t%2Acos%28t%29+%29+

   %28dy%29%2F%28dt%29+=+2%28t%29%28-t%2Asin%28t%29++%2B+2%2Acos%28t%29+%29+

   %28dy%29%2F%28dt%29+=+2t%28-t%2Asin%28t%29++%2B+2%2Acos%28t%29+%29+

   %28dy%29%2F%28dt%29+=+2t%282%2Acos%28t%29+-+t%2Asin%28t%29%29+



ii) y+=+%28cos%28t%29%29%2F%28sin%28t%29%29 

    y+=+cot%28t%29

    %28dy%29%2F%28dt%29+=+-csc%5E2%28t%29

iii) +y+=+e%5E%28pi%2At%29+-+e%5E%28-pi%2At%29 

  %28dy%29%2F%28dt%29+=+pi%2Ae%5E%28pi%2At%29+-+%28-pi%29%2Ae%5E%28-pi%2At%29

  %28dy%29%2F%28dt%29+=+pi%2Ae%5E%28pi%2At%29+%2B+pi%2Ae%5E%28-pi%2At%29

  +%28dy%29%2F%28dt%29+=+pi%28e%5E%28pi%2At%29+%2B+e%5E%28-pi%2At%29%29

Edwin