find dy/dx by implicit differentiation

Question

a) 3xy=4+y^2

b)sinx-3cos2y=5

Answer 1

(a)

3xy = 4 + y²

Implicit differentiation is used when the given relation of the form . In this case, it may be inconvenient or even impossible to solve for y as a function of x . So in such cases it is convenient to use Implicit differentiation .

Apply the formula 

3xy' + 3y (1) = 0 + 2y y'

3xy' - 2y y' = -3y

Take the term y' common 

y'(3x - 2y) = -3y

y' = -3y / (3x - 2y)

y' = 3y / (2y - 3x)

Answer 2

(b)

sinx - 3cos2y = 5

6 sin 2y y' = -cos x

y' = -cosx/6 sin 2y

y' = -cosx/6 sin 2y