Question

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).

Answer #1

given that

x^2*y^3 + 3y^2 - 5x = -10

Using Implicit differentiation:

2x*y^3 + x^2*3*y^2*(dy/dx) + 3*2*y*(dy/dx) - 5*1 = 0

dy/dx*(3x^2y^2 + 6y) = 5 - 2xy^3

dy/dx = (5 - 2xy^3)/(3x^2y^2 + 6y)

Part B.

ow slope of tangent line,going through point (1, 2) will be:

m = (dy/dx)_(1, 2)

m = (5 - 2*1*2^3)/(3*1^2*2^2 + 6*2) = -11/24

Now equation of tangent line will be:

(y - y1) = m*(x - x1)

(y - 2) = (-11/24)*(x - 1)

y - 2 = -11*x/24 + 11/24

24y - 48 = -11x + 11

**11x + 24y - 59 = 0**

**y = -11x/24 + 59/24**

**Let me know if you've any query.**

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)

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

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)

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...

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

Find dy/dx by implicit differentiation:
A.). x^4 + y^3 = 3
B.). 5x^2 +3xy - y^2 =7
C.) x^3(x+y) = y^2(4x-y)

Find dy dx/dy implicit differentiation. (x + y^2)10 = 9x^2 +
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Use implicit differentiation to determine dy/dx given the
equation e^x⋅y^3+x^4=sin(y)
dy/dx=

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6sin(2x+3y)=7xy

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(x+y)4=4y-9x

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