Question

Consider x^2 +sin(y)=4xy^2 +1

a.)Use Implicit differentiation to find dy/dx

b.) find an equation tangent of the line to the curve x^2 +sin(y)=4xy^2 +1 at (1,0)

Answer #1

Using implicit differentiation complete the following:
A) Find dy/dx of x^3 + y^3 =4xy
B) Find the equation of the tangent line to the curve at the
point (1,1) in slope-intercept form
C) Find the equation of the normal line to the curve at the
point (1,1) in slope- intercept form

Use implicit differentiation to find dy dx for x^2 y^3 + 3y^2 −
5x = −10.
(b) Find the equation of the line tangent to the curve in part
a) at the point (1, 2).

Use Implicit Differentiation to find first dy/dx , then the
equation of the tangent line to the curve x2+xy+y2= 2-y at the
point (0,-2)
b. Determine a function of the form f(x)= ax2+ bx + c (that is,
find the real numbers a,b,c ) if the graph of the function has
slope 2 at the point (3,4) , and has a horizontal tangent where
x=1
c. Assume that x,y are functions of variable t satisfying the
equation x2+xy=10. Find dy/dt...

3. Consider the equation:
x^2y −√y = 2 + 4x^2
a) Find dy/dx using implicit differentiation. b)Construct the
equation of the tangent line to the graph of this equation at the
point (1, 9)

A) Use implicit differentiation to find an equation of the
tangent line to the ellipse defined by
5x^2+4xy+3y^2=12 at the point (−1,−1)
B) Find dy/dx by implicit differentiation, if ey=2x−2y

Use implicit differentiation to find an equation of the line
tangent to the curve sin(x+y)=2x-y at the point (pi,2\pi )

Use implicit differentiation to determine dy/dx given the
equation e^x⋅y^3+x^4=sin(y)
dy/dx=

Use implicit differentiation to find an equation of the line
tangent to the curve sin(x+y)=2x-y at the point (pi, 2pi )

Use implicit differentiation to find an equation of the tangent
line to the curve 3xy^3+4xy=56 at the point (8,1)

Find dy dx/dy implicit differentiation. (x + y^2)10 = 9x^2 +
2

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