Charmaine, Chavez, and Lauren's Jeopardy

Derivative Rules

100

d/dx sin(x) 

cos(x)

200

d/dx tan(x) 

sec^2 x

300

d/dx lnx

1/x

400

d/dx cot^-1 x

-1/1+x^2

500

d/dx csc^-1 x

-1/(|x|sqrt(x^2 -1))

Order of Reasons

100

What rule to solve d/dx 5x?

Constant Rule

200

3x-arcsinx

derivative of 3x subtracted by derivative of arcsinx

300

What is the overarching rule used to find the derivative without logarithmic differentiation? ((5x-50/x)(arctanx+2x))/(19sin(cos(x)))

Quotient Rule 

400

How can you solve this problem without using quotient rule: (x⁵-2x³-8x²)/x

Simplify then use the power rule.

500

How could you solve this problem without using quotient rule or logarithmic differentiation: sinx/3x²

Product Rule. Manipulate the equation to make it sinx(3x^-2) then you can do the normal operations for product rule.

Logarithmic/Implicit Differentiation

100

y=(cosx)⁷

((-7sinx)/(cosx))((cosx)⁷)

200

use logarithmic. x^3y+y²-x²=5

-4/5

300

y=x³⋅e^2x, find dy/dx. use implicit differentiation. 

dy/dx = 3x² e^2x+2x³e^2x

400

y= sqrt(x)⋅ln(x). use logarithmic differentiation. 

dy/dx = (1+2ln(x))/2sqrt(x)

500

sin2x²y³= 3x³+1. Find dy/dx using implicit. 

dy/dx = (9x-4y³cos2x²y³)/(6xy²cos2x²y³)

Solve the Equation

100

find the slope x² +y²=25 at (3,-4)

3/4

200

find dy/dx given y² =3xy+siny

dy/dx=3y/(2y-3x-cosy)

300

Find (dy/dx) given x²y + xy² =6 

(2xy + (y^2))/(x^2) +2xy

400

Find the tangent line at xsin2y = ycos2x 

at (pi/4, pi/2)

y- (pi/2) = 2(x- (pi/4))

500

Find the normal and tangent line at x² +xy -y²=1

at (2,3)

Tangent: y-3= (7/4)(x-2)

Normal: y-3= (-4/7)(x-2)

Vocab

100

When do you use logarithmic differentiation?

Whenever you want (products + quotients) 

200

Another word for derivative

instantaneous slope

300

What is differentiation

The act of finding the derivative

400

Which one would you use the product rule for?

9(x+1) or x(x +1)

x(x+1)

500

Difference between implicit and explicit differentiation

Implicit: y is wrapped up into problem

Explicit: Gives us y clearly