D(DMV)'s FUN Jeopardy Game!!!!!!!

Chain Rule

100

Find the derivative of f(x) = (x-5)⁴

What is "4(x-5)³"

200

Find the derivative of f(x) = 2(x³-4)⁵

What is "10(x³- 4)⁴ * 3x²"

300

Find the derivative of f(x) =2(5x² - 4(3x³ -5x))³

What is "6(5x²-4(3x⁴-5x))²*10x-36x²+20"

400

 Find the derivative of f(x) =2x

this is not chain rule

500

Find the derivative of the function: f(x)=3sin(5+2x²)

What is "12xcos(5+2x²)"?

Inverse Functions

100

The function f is defined by f(x)=x³+2x²+4x and f(-2)=-8. if g is the inverse function of f, what is the value of g'(-8)?

g'(-8)=1/8

200

The function f is defined by f(x)= -2x³-3x²-4x. if g is the inverse function of f and g(3) = -1, what value of g'(3)?

g'(3)=-1/4 

300

the table below gives selected values for the differetiable and decreasing function f and its derivative. if f^-1 is the inverse function of f, what is the value of (f^-1)'(-4)?

    x      |        f(x)        |       f'(x)

   -4      |        10         |        -8

   -1      |         5          |        -5

    0      |          0          |       -2

   10     |         -4          |      -10

(f^-1)'(-4)=-1/10

400

the function f is defined by f(x)=-2x³-2x+5 and f(0)=5. if g is inverse function of f, what is the value of g'(5)?

g'(5)=-1/2

500

the function f is defined by f(x)= -x³-3x-4 and the point (1,-8) is on graph of f. if f^-1 is the inverse function of f, what is the value of (f^-1)'(-8)?

(f^-1)'(-8)=-1/6

Symbolic Differentiation

100

x | f(x) | f'(x) | g(x)| g'(x)|    Given h(x)= f(x) * g(x)

4 |  8   | 5 |   6 | -5 |             find h'(3)  

1 | -8 | -6| -1 | 7|

3 | -4  | -7| 1 | 4|

What is -100/3?

200

Approximate f'(3), using the table below of the x and f(x) values

x    0    1     2      3     4

f(x) 0    1     4      9     16

What is f'(3) (approximately equals) 6

300

J'(-1) where J(x) = f(g(x))

x      f(x)      f'(x)      g(x)      g'(x)

-1     5          2           3           4

3      -2         -4          -1          0

What is J'(-1) = f'(3) * g'(-1)?

400

Find the equation of the tangent line at x= -1, if H(x)= 3f(g(x))

x  |   f(x)   |  f'(x)   |  g(x)  |   g'(x)

-1     -2         4           -1          2 

0      4          3            2          -3

2      3          -2          -4          1

What is y= 24(x+1)-6?

500

Find K'(3) where K(x)= f(x)/g(x)²

x       f(x)      f'(x)       g(x)          g'(x)

3         4         2           -1              3

 What is K'(3) = 2 +24 = 26?

Derivatives of Inverse Trig Functions

100

d/dx arcsin(5x) 

what is dy/dx = 5/√1-25x²

^{(the entire denominator is under the square root)} 

200

d/dx arctan(2x)

2/4x²+1

300

d/dx arcsec(x³)

3/|x|√x³-1

400

d/dx arccsc(4x⁵)

-5/|x|√16x¹⁰-1

500

d/dx arccot(4x⁴)

what is d/dx = -16x³/16x⁸+1

Implicit Differentiation

100

what is dy/dx = -5x/3y2

 5x²+2y³=4

200

5y²+3=x²

what is dy/dx = x/5y

300

sin(x+y) = 2x

what is dy/dx = 2sec(x+y)-1

400

x/siny = 5 

 what is dy/dx = sin(y) / xcosy or tan y /x

500

x³+y³=6xy

what is dy/dx = 2y-x²/y²-2x