What's the Rule(s)?
Derive it!
Tangent Lines
100

y = x/(x+1)

quotient rule

100

y = 5

y' = 0

100

F(x) = 100 at x = 4

y = 0x +100

200

y = x2

power rule

200

f(x) = 200x7

f'(x) = 1400x6

200

f(x) = 4x2 + 12x + 2 at x = 2

y = 28x - 14 

300

y = xsin(x)

product rule


300

f(x) = sin(x)cos(x)

f'(x) = cos2(x) - sin2(x)

300

y = 2xsin(x) at x = pi


y = (-2pi)x + 2(pi)2

400

f(x) = xsin2(x)

product rule and chain rule

400

f(x) = (x2 + 2x)/sin(x)   (Don't try to simplify)

f'(x) = [(2x+2)sin(x) - (x2 + 2x)cos(x)]/sin2(x)

400

y = (x3 - x2)2 at x = 2


y = 64x -112

500

f(x) = xcos(x)/(x+1)2

quotient rule, product rule, chain rule

500

y = (3x2)/(xsin(x))

y' = (3sin(x) - 3xcos(x))/sin2(x)

500

y = cos2(x)/(x3 + 2) at x = 0   (Hint: don't foil)


y = 0x + 1/2

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