Basic Derivative Information and Power Rule
Chain Rule
Product & Quotient Rules
Applications
Trig Derivatives
100
The derivative calculates the ________.
Slope
100
Define the Chain Rule for f(g(x))
g′(x)f′(g(x))
100
Define the Product Rule using f(x)g(x)
f′(x)g(x)+ g′(x)f(x)
100

 A 13 ft ladder is leaning against a wall and sliding towards the floor.  The top of the ladder is sliding down the wall at a rate of 7 ft/sec. How fast is the base of the ladder sliding away from the wall when the base of the ladder is 12 ft from the wall?

What equation best represents this related rates problem? 

a2+b2=c2

100
d/dx cosx=
-sinx
200
d/dx 5 =
0
200
d/dx (3x+1)²
6(3x+1)
200
f(x)=x²sinx, what is f′(x)?
2xsinx+ x²cosx
200

Oil spills and spreads in a circle on the surface of the ocean.  The radius of the spill increases at a rate of 2 m/min.  How fast is the area of the spill increasing when the radius is 13 m?

What does the 2 m/min represent?

dr/dt

200
Differentiate y=tan(x)
y′ =sec²(x)
300
d/dx x² =
2x
300
d/dx sin(4x²)
8xcos(4x²)
300
Differentiate y=x³lnx
y′ =x²(1+3lnx)
300

A spherical balloon is deflated so that its radius decreases at a rate of 4 cm/sec.  At what rate is the volume of the balloon changing when the radius is 3 cm?

dv/dt = -144pi

300
Differentiate y=csc(x)
y′ =-csc(x)cot(x)
400
d/dx 3x²-x+3 =
6x-1
400
Differentiate y=√13x²-5x+8
y′ =26x-5/ 2√13x²-5x+8
400
Differentiate y=e^-x²cos2x
y′ =−2xe^(−x²) cos2x−2e^(−x²)sin2x
400

A hypothetical cube shrinks so that the length of its sides are decreasing at a rate of 2 m/min. At what rate is the volume of the cube changing when the sides are 2 m each?

Volume of cube = s3      (s is the side length)

-24 m3/min

400
d/dx sin(2x)
2cos(2x)
500
Speed is _________.
the absolute value of velocity
500
Differentiate y=3tan√x
y′ =3sec²√(x)/ 2√x
500

f(x)= (x²-1)³/ x²+1, what is f′(x)?

f′(x)= [6x(x2-1)(x2+1)-2x(x2-1)3] / (x²+1)²

500

Water leaking onto a floor forms a circular pool.  The area of the pool increases at a rate of 25π cm²/min.  How fast is the radius of the pool increasing when the radius is 6 cm?

25/12 cm/min
(approx.  2.0833)

500

d/dx sin(x)cos(x)=

cos2x-sin2x

M
e
n
u