please solve or send me examples of how to solve the following calculus probs.

Question

Assuming that each equation in problems 1-12 defines a differentiable function of x, find D_xy by implicit differentiation.

1. Y² – x² = 1

 

1. 9x² + 4y² = 36

 

1. xy = 1

 

1. X2 +  ²y² = 4 ², where  is a constant.

 

1. Xy² = x – 8

 

1. X² + 2x²y + 3xy = 0

 

1. 4x³ + 7xy² = 2y³

 

1. X²y = 1 + y²x

 

1.  + 2y = y² + xy³

 

1. x  + 2y = y² + xy³

 

1. xy + sin(xy) = 1

 

1. cos(xy²) = y² + x

 

1. e^2x+3y = x² – ln(xy³)

 

1. x²tan(y) + y¹⁰sec(x) = 2x

 

 

 

 

 

in problems 15-20, find the equation of the tangent line at the indicated point.

1. X³y + y³x = 30; (1 , 3)

 

1. X2y2 + 4xy = 12y; (2 , 1)

 

1. Sin(xy) = y; (π/2 , 1)

 

1. y + cos(xy²) + 3x² = 4; (1 , 0)

 

1. x^2/3 – y^2/3 – 2y = 2; (1 , -1)

 

1. √x + xy² = 5; (4 , 1)

In problems 21-32, find dy/dx

1. y = 3x^5/3 +

 

1. y = ∛x – 2x^7/2

 

1. y = ∛x + √x

 

1. y = ∜(2x + 1)

 

1. y = ∜(3x² - 4x)

 

1. y = (x³ – 2x )^1/3

 

1. y = 1 / (x3 + 2x)^2/3

 

1. y = (3x – 9)^-5/3

 

1. y = √(x² + sinx)

 

1. y = √(x²cosx )

 

1. y = 1 / (∛(x²sinx))

 

1. y = ∜(1 + sin5x)

 

Answer 1

9x^2 +4 y^2=36 is ellips around (0,0)

majer axis=x & x-length=6

y-length=4