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Homework Help: calculus

Posted by Sasha on Thursday, October 14, 2010 at 12:12pm.

A. find y' by implicit differentiation.
B. solve th equation explicitly for y and differentiate to get y' in terms of x.

cos (x) + √y = 5

• calculus - Reiny, Thursday, October 14, 2010 at 12:19pm

  a)
  - sin(x) + (1/2)y^(-1/2)dy/dx = 0
  -(1/4)(1/√y)dy/dx = sin(x)
  
  dy/dx = -4√y sin(x)
  
  b)
  √y = 5 - cosx
  y = 25 - 10cosx + cos^2 x
  dy/dx = -10cosx + 2(cosx)(-sinx)
  = -2cosx(5cos(x) + 2sin(x))
  

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