Double Jeopardy Calculus Derivatives Review

Applications of Derivatives

200

The slope of the tangent line equaling this number would mean a max or min at that point ?

0

400

This is used to determine the concavity of a function

The second derivative

600

Besides the derivative equaling 0, there must also be a _________________ for the function to have a maximum. 

sign change

800

How is acceleration related to position?

second derivative

1000

The third derivative of position is 

jerk

Product and Quotient Rule

200

Find the derivative of y = 3x⁴*sin x

4x³ sin x + 3x⁴ cos x

400

f(x) = (3x - 2x²)/(5 + 4x)

(-8x²-14x+15)/(5+4x)²

600

Find the derivative of y = ln(4x²)/e^6x

(2/e^6x)-(((6xln(4x²))/(e^6x))

800

Daily Double

Calculate the derivative of (csc(x²)tan(x²))/-sec(x²)

0

1000

(lnx*sinx³)/log₃(x²)

(((1/x*cos(x³)-3x²lnx*sin(x³))/log₅x²)-

(((2/ln5)*lnxcos(x³))/(log₅x²)²

Chain Rule

200

Find y' if y = (3x² - 5)⁶

36x(3x² - 5)⁵

400

Find the derivative of f(x) = tan(7x⁵+3x)

(35x⁴+3)sec²(7x⁵+3x)

600

Find y' if y = 1/(9x² + 4)^1/2

-(18x)/(9x² + 4)^3/2

800

f(x) = log₈(cos(x²))  Find f'(x)

(-2/ln8)*x*tanx²

1000

Differentiate: 3^{sec(5x^3)}

15ln3x*3^sec(5x^3)*sec(5x^3)tan(5x^3)

Implicit Differentiation

200

Find the derivative implicitly x⁴ + y² = 2x

y' = (1/y)-(2x³/y)

400

x²y+y = 6

y' = (6-2xy)/(x²+1)

600

(4y - 2)³ = 6x - 12

y' = 1/(2(4y - 2)²)

800

tan(xy)+sin(y²)= 4

y' = (-ysec²(xy))/(xsec² (xy)+ 2cos(y²))

1000

xsin(x³)+3ycos(y²)=y³

(sin(x³)+3x³*cos(x³))/(3y²+6y²*sin(y²)-3cos(y²))

Trig Derivatives

200

Derivative of secx

secxtanx

400

Daily Double

csc(x³)

-3x²csc(x³)cot(x³)

600

Derivative of sin^-1x

1/(1-x²)^1/2

800

Derivative of tan^-1x

1/(1+ x²)

1000

Derivative of sec^-1(5x²)

10x/ (l5x²l ((25x⁴-1)^1/2)