Question

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 d/dx (tan−1 (x)) = 1 / 1+x^2 .

Answer #1

Differentiate the function
y=ln(e-x +xe-x)
Find y and y"
y=ln(sec(3x)+tan(3x))
Use logarithmic differentiation to find the derivative
of the function.
y=(cos(9x))x
Use logarithmic differentiation to find the derivative
of the function.
y=(sin(9x))(lnx)

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 logarithmic differentiation
1. y = (sin(2x))^x
2. y =(3^x)/(1 + 3^x)
3. y= (x+1)^(tan(x))

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:

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)

(a) Find an equation of the plane tangent to the surface xy ln x
− y^2 + z^2 + 5 = 0 at the point (1, −3, 2)
(b) Find the directional derivative of f(x, y, z) = xy ln x −
y^2 + z^2 + 5 at the point (1, −3, 2) in the direction of the
vector < 1, 0, −1 >. (Hint: Use the results of partial
derivatives from part(a))

If 5x^2+3x+xy=3 and y(3)=-17, find y'(3) by implicit
differentiation.
Thus an equation of the tangent line to the graph at the point
(3,-17) is

Write an equation for the tangent line to the plane curve xy^2 −
2x^2 + 3 x + y = 7 at the point P .(1,-3)

Answer each of the questions below. (a) Find an equation for the
tangent line to the graph of y = (2x + 1)(2x 2 − x − 1) at the
point where x = 1. (b) Suppose that f(x) is a function with f(130)
= 46 and f 0 (130) = 1. Estimate f(125.5). (c) Use linear
approximation to approximate √3 8.1 as follows. Let f(x) = √3 x.
The equation of the tangent line to f(x) at x =...

please only answer if you can do all parts, show work and circle
answer
part 1)
Use implicit differentiation to find the first derivative of y
with respect to x.
ln(4y)=5xy
dy/dx=
part 2)
Find dy/dx by implicit differentiation.
3+8x=sin(xy^2)
Answer: dy/dx=
part 3)
Find dy/dx by implicit differentiation.
e^((x^2)y)=x+y
dy/dx=
part 4)
Find dy/dx by implicit differentiation.
sqrt(x+y)= 9+x^2y^2
dy/dx=
part 5)
Find dy/dx by implicit differentiation.
e^y=8x^2+7y^2
dy/dx=

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