Finding the derivative

Question

1) Find dy/dx for e^(x+y)=y

 

2) y=csc(5x^4)

 

 

Answer 1

1.  y = e^xe^y

  y' = dy/dx = e^xe^y + e^xe^yy'  using the product rule

  y' (1-e^xe^y) = e^xe^y

  y' = e^xe^y /  (1-e^xe^y)  and this can be simplified in various ways, according to taste.

2.  Easy...just look up what the derivative of cosec is, and then apply a factor 5,attributed to the chain rule, deriv of argument.