Basic Derivative Information and Power Rule
Chain Rule
Product Rule
Quotient Rule
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
Define the Quotient Rule using f(x)/g(x)
[g(x)f′(x) - f(x)g′(x)]/ (g(x))²
100
d/dx cosx=
-sinx
200
d/dx 5 =
0
200
d/dx (3x+1)²
6(3x+1)
200

f(x)=x²(x3+4x2-4x+5), what is f′(x)?

2x(x3+4x2-4x+5)+x²(3x2+8x-4)

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

Differentiate y=(2x3-5x)(sinx)

y′ =(6x2-5)sinx+cosx(2x3-5x)

300

Differentiate y= (1+4x2) / (x²-sinx)

y′= [(8x)(x²-sinx)] - [(2x-cosx)(1+4x2) / (x²-sinx)²

300

Differentiate y=cos(x)

y′ =-sin(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=(x2/3)(cosx)

y′ =-sinx(x2/3)+(cosx)(2/(3x1/3))

400

f(x)= (x²-1)/ x²+1, what is f′(x)?

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

400
d/dx sin(2x)
2cos(2x)
500
Speed is _________.
the absolute value of velocity
500

Differentiate y=3sin(√x)

y′ =3cos(√(x))/ 2√x

500
Differentiate y=x²sin³(5x)
y′ =xsin²(5x)[15xcos(5x)+2sin(5x)]
500

f(x)= (x²-1)³/ x²+1, what is f′(x)?

f′(x)= [4x(x²-1)²(x²+2)] / (x²+1)²

500

d/dx sin(x3-2x)

(3x2-2)cos(x3-2x)

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