Basic Derivative Information and Power Rule
Chain Rule
Product Rule
Quotient Rule
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

Define the Quotient Rule using f(x)/g(x)

[g(x)f′(x) - f(x)g′(x)]/ (g(x))²

200
d/dx 5 =
0
200
d/dx (3x+1)²
6(3x+1)
200

Differentiate the Product

y=x^2(3x+1)

9x^2+2x

200

Differentiate y= 2/(x+1)

y′ = -2/ (x+1)²

300
d/dx x² =
2x
300
d/dx sin(4x²)
8xcos(4x²)
300

Differentiate 

(2x+1)(3x-2)

12x-1

300
Differentiate y= (1+lnx) / (x²-lnx)
y′= [(1/x)-x-2xlnx] / (x²-lnx)²
400
d/dx 3x²-x+3 =
6x-1
400
Differentiate y=√13x²-5x+8
y′ =26x-5/ 2√13x²-5x+8
400

Differentiate 

f(x)=(-3+x^-3)(-4x^3+3)

-9x^-4 -36x^2

400

f(x)= (x²-1)³/ x²+1, what is f′(x)?

f′(x)= [4x(x²-1)²(x²+2)] / (x²+1)²

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

Differentiate 

y=x^4(x^3-2x^2+3x-1)

7x^6-12x^5+15x^4-4x^3

500
Differentiate y= (x³lnx)/(x+2)
y′ = [x²(2xlnx+6lnx+x+2)]/ (x+2)²
M
e
n
u