Question

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

Answer #1

We are given equation as

we can find derivative with respect to x on both sides

we can solve for y'

now, we can plug back x=pi and y=2pi

so, slope is undefined

so, tangent line is vertical line

so, the equation of tangent line is

**.......Answer**

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 find an equation of the tangent
line to the curve at the given point.
x2+y2=(2x2+4y2-x)2
(0, 0.25)
(cardioid)
y=?

Use implicit differentiation to find an equation of the tangent
line to the curve at the given point. 3(x2 + y2)2 = 25(x2 − y2) (2,
1) (lemniscate) y= ?

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)

3. Find the equation of the tangent line to the curve 2x^3 + y^2
= xy at the point (−1, 1).
4. Use implicit differentiation to find y' for sin(xy^2 ) − x^3
= 4x + 2y.
5. Use logarithmic differentiation to find y' for y = e^4x
cos(2x) / (x−1)^4 .
6. Show that d/dx (tan (x)) = sec^2 (x) using only your
knowledge of the derivatives of sine/cosine with derivative
rules.
7. Use implicit differentiation to show that...

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

4) Use implicit differentiation to find the equation of the
tangent line to the curve xy^3+xy=16 at the point (8,1). The
equation of this tangent line can be written in the form
y=mx+by=mx+b where m is:
and where b is:

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...

use implicit differentiation to find the slope of the
tangent line to the curve defined by xy^9+5xy=36 at the point
(6,1)

find an equation for the line tangent to the given curve at the
point defined by the given value of t.
x sin t + 2x =t, t sin t - 2t =y, t=pi

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