Test 3

Implicit Deficit

100

Use implicit differentiation to find y'

x²+y²=9

What is 

y'= - x / y

200

Find y' using implicit differentiation

x / y³ = 1

What is

y' = y / 3x 

300

Use implicit differential to find the derivative

tan^-1y=ln(x)

What is 

dy/dx = (1+y²) / x

400

Find y' by implicit differentiation for 

e^x - sin(y) = x

What is 

y' = - (1-e^x) / cos(y)

OR 

y' = (e^x - 1) sec(y)

500

Use implicit differentiation for find y'

x³y⁵ + 3x = 8y³ + 1

What is 

y' = (3x² y⁵ + 3) / (24y² - 5x³ y⁴)

Inverse esrevnI

100

Evaluate cos^-1( - √2 / 2 )

What is y = 3π / 4 ?

200

Differentiate

T(x) = 2cos(x) + 6cos^-1(x)

What is 

T'(x) = -2sin(x) - 6 / √(1-x2)

300

Differentiate: 

y= √x sin^-1(x)

What is 

y' = (1/2) x^-1/2 sin^-1(x) + ( √x / √(1-x²) )

400

Differentiate:

f(w) = sin(x) + x²tan^-1(x)

What is 

f'(x) = cos(x) + 2x tan^-1(x) + (x² / (1+x²) )

500

Differentiate: 

h(x) =  tan^-1(x) + 4cos^-1(x)

What is 

h'(x) = 1/ (1+x2) - ( 4 / sqrt (1-x2))

Logged Out

100

Differentiate 

F(x)=4^x - 5log₉x

What is 

F'(x) = 4^x ln 4 - 5/(x ln9)

200

Differentiate 

f(x) = 3e^x + 10x³lnx

What is 

f'(x)= 3e^x + 30x² lnx + 10x²

300

Differentiate

y = 5e^x / (3e^x+1)

What is

y' = 5e^x / (3e^x + 1)²

400

Differentiate 

f(t) = (1 + 5t) / ln(t)

What is 

f'(t) = (5ln(t) - (1/t) - 5) / (ln(t))²

OR 

f'(t) = (5ln(t) - (1/t)(1+5t)) / (ln(t))²

500

Determine if V(t) is increasing or decreasing at the following point.

V(t) = t / e^t @ t=-4

What is increasing @ t=-4? 

Relating(Calculator)

100

In the following, assume that x and y are both functions of t. Given x = -2, y =1, and x' = -4, determine y' for the following equation. 

6y² + x² = 2 - x³ e^{4 - 4y}

What is 

y' = 8/11

200

In the following, assume that x, y, and z are all function of t. Given x = 4, y = -2, z = 1, x' = 9, and y' = -3, determine z' for the following equation

x(1 - y) + 5z³ = y²z² + x² - 3

What is 

z' = 45 / 7

300

A person is standing 350 feet away from a model rocket that is fired straight up into the air at a rate of 15 ft/sec. At what rate is the distance between the person and the rocket increasing at 20 seconds?

What is 

z' = 9.76187

400

A thin sheet of ice is in the form of a circle. If the ice is melting in such a way that the area of the sheet is decreasing at a rate of 0.5 m²/sec, at what rate is the radius decreasing when the area of the sheet is 12 m²? (USE CALCULATOR)

What is 

r' = -0.040717?

500

Two people are at an elevator. At the same time one person starts to walk away from the elevator at a rate of 2 ft/sec and the other person starts going up in the elevator at a rate of 7 ft/sec. What rate is the distance between the two people changing 15 seconds later?

What is 

z' = 7.2801

Linear I ate a ton

100

Find a linearization of 

f(x) = 3xe^2x-10 @ x=5

What is 

L(x) = 33x - 150

200

Find the linearization of 

h(t) = t⁴ - 6t³ + 3t - 7 @ t=-3

(USE CALCULATOR)

What is 

L(t) = -267t - 574

300

What is the linearization of 

f(x) = x^1/3 @ x = 8

What is 

L(x) = (1/12) x + 4/3

400

What is the linearization of 

g(z) = z^1/4 @ z = 2

What is 

L(z) = 2^1/4 + (1/4) (2^-3/4) (z - 2) 

500

Find linearization of 

f(t) = cos(2t) @ t = 1/2

(USE CALCULATOR)

What is 

L(t) = cos(1) - 2sin(1) (t - 1/2) 

OR

L(t) = 0.5403 - 1.6829 (t - 1.2)