Test 3! WOOO!

Log: The "Why can't I solve this normally?" Method

100

y = x²(x+1)³

y'=y(2/x + 3/(x+1))

200

y=(x-2)⁴/(x³)

y'=y(4/(x-2) - 3/(x))

300

y=(x²+1)⁵(x-1)

y'=y(10x/(x²+1) +1/(x-1))

400

y = x⁵/(x+3)²

y'=y(5/x - 2/(x+3))

500

y=(x-1)²(x+2)3

y'=y(2/(x-1) + 3/(x+2))

Arc you serious right now?

100

y=sin^-1(2x)

y'=2/sqrt(1-4x²)

200

y=tan^-1(3x)

y'=3/sqrt(1+9x²)

300

y=cos^-1(x²)

y'=-2x/sqrt(1-x⁴)

400

y=tan^-1(sqrt(x))

y'=1/(2sqrt(x)(1+x))

500

y=sin^-1(x³)

3x²/sqrt(1-x⁶)

We can't solve for y and we are NOT happy about it!

100

x²+y²=25

y'=-x/y

200

x³+y³=6xy

y'=3/(1+9x²)

300

x²y+y²=7

y'=-2x/sqrt(1-x⁴)

400

x²+xy+y²=9

y'=(-2x-y)/(x+2y)

500

e^x+y²=xy

y'=(e^x-y)/(2y-x)

We went on a tangent, and somehow found a line.

100

Tangent line of x²+y²=25 at (3,4)

y-4=(-3/4)(x-3)

200

Normal Line of x²+xy+y²=7 at (2,1)

y-1=(4/5)(x-2)

300

Tangent Line of x³+y³=9 at (2,1)

y-1=-4(x-2)

400

Normal Line of x²y+y²=6 at (1,2)

y-2=(5/8)(x-1)

500

Tangent Line of x²+y²=8 at (2,2)

y-2=-(x-2)

Wait, they are allowed to use sentences in math!?!

100

A balloon rises at 6 ft/s from a point 10 ft away. Find d𝛳/dt when height = 10sqrt(3) ft.

1/40 rad/s

200

A balloon rises at 4 m/s from a point 5 m away. Find d𝛳/dt when height = 5sqrt(3) m.

1/20 rad/s

300

A spherical balloon expands so dr/dt = 2 cm/s. Find dV/dt when r = 6 cm.

288𝜋 cm³/s

400

A circular puddle’s area increases at 8 square inches/second. Find dr/dt when r = 4 in.

1/𝜋 in/s

500

A ladder 10 ft long slides away at 2 ft/s. How fast is the top falling when the bottom is 5sqrt(3) ft away from the wall?

-4 ft/s