AB Calculus: Chapter 4 Jeopardy

Product Rule or Quotient Rule

100

Find y' if y = 4x³cos(7x).

y'=12x²cos(7x)-28x³sin(7x)

200

Find y' if y = (x+5)/(x-2)

y' = -7/(x-2)²

300

Find y' in factored form if y = (x+3)⁴(5x-2)⁷

y'=(x+3)³(5x-2)⁶(55x+97)

400

Find y' if y = sin(3x)/cos(3x)

y' = 3sec²(3x)

500

Find y' in factored form if y = x √(25-x²)

y' = (25-x²)^-1/2(25-2x²)

Implicit Differentiation

100

Find y ' if x^1.2+y^1.2=64

y' = -x^.2/y^.2

200

Find y' if 4x+8x²y⁶+y⁴=21³

y'=(-1-4xy⁶)/?(12x²y⁵+y³)

300

Find y' if 9x²-20xy+25y²=12

y'=(10y-9x)/(25y-10x)

400

Find y': cos(xy) = x+y

y'=(-ysin(xy)-1)/(1+xsin(xy))

Trig Derivatives

100

Find y' if y=cot(5x).

y'=-5csc²(5x)

200

Find y if dy/dx=csc(5-x)cot(5-x)

y=csc(5-x)+C

300

Find y' if y=√(tan(2x)).

y' = (tan(2x))^-1/2sec²(2x)

400

Find y' if y = sec⁵(x²)

y'=10xsec⁵(x²)tan(x²)

500

Is y=cot(3x) increasing or decreasing at x=5? Why?

y'(5)=-7.094 so it is decreasing.

Inverse Trig Derivatives

100

Find y' if y=sin^-1(3x).

y'=3/√(1-9x²)

200

Find y' if y=cos^-1(x²).

y'=-2x/√(1-x⁴)

300

Find y' if y=tan^-1√(x).

y'=(.5x^-1/2)/(1+x)

400

Find y' if y=4sec^-1(x/2).

y'=2/(abs(x/2)√(x²/4-1)

500

f(x) has a finite limit as x->6, but f(6) is undefined. Is f(x) differentiable? Why?

No, not continuous -> not differentiable.

Parametrics

100

Find dy/dx:
x=sec(2t)
y=tan(2t3)

dy/dx=(3t²sec²(2t³))/(sec(2t)tan(2t))

200

Find dy/dx:
x=cos(t)+tsin(t)
y=sin(t)-tcos(t)

dy/dx=tan(t)

300

Find dy/dx:
x=8cos3(t)
y=8sin3(t)

dy/dx=-tan(t)

400

Find dy/dx:
x=2atan(t)
y=2acos2(t)
(a is a constant)

dy/dx=-2cos³(t)sin(t)

500

f(x) = ax3, x≤1
                  (bx-2)2, x>1
Find a and b so f is differentiable.

a=16 and b=6