Calculus Question

Question

Find the derivative of the following using implicit differentiation:

 

A) x = sin y + cos x

B) xy-y³=sinx

Help!?

Answer 1

A)    1 = cos y * y' - sin x

 

        so   (1 + sin x)/cos y  =  y'

 

B)  xy' + y - 3*y^2 *y' = cos x

 

     xy' - 3*y^2*y' = cos x - y

 

     y' (x - 3*y^2) = cos x - y

 

     y' = (cos x - y)/(x - 3*y^2)

              

Answer 2

A) x = sin y + cos x

 

1 = (cos y) dy/dx - sin x

 

(cos y) dy/dx = 1 + sin x

 

dy/dx = (1 + sin x) / cos y

 

 

B) xy - y³ = sin x

 

y + x dy/dx - 3y² dy/dx = cos x

 

(x - 3y²) dy/dx = -y + cos x

 

dy/dx = (y - cos x) / (3y² - x)