A. find y' by implicit differentiation.

Question

B. solve th equation explicitly for y and differentiate to get y' in terms of x.

cos (x) + √y = 5

Answer 1

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))