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 u and v

f'(uv)=u'v+uv'

100

Define the Quotient Rule using u and v

f'(u/v)= (u'v-uv')/v^2

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
Differentiate y= 2/(x+1)
y′ = -2/ (x+1)²
200
Differentiate y=tan(x)
y′ =sec²(x)
300
d/dx 3x²-x+3 =
6x-1
300

Differentiate y=√13x²-5x+8

y′ =26x-5/ 2√13x²-5x+8

300

Differentiate y=(5x^2)(ln(x))

y′ = 5x(2lnx+1)

300
f(x)= (x²-1)³/ x²+1, what is f′(x)?
f′(x)= [4x(x²-1)²(x²+2)] / (x²+1)²
300

d/dx cot(x)

-1/x^2+1

400

If g is the inverse of f (which means the f(g(x))=x and g(f(x))=x), and f(12)=4, f'(12)=-5, find g(4) and g'(4).

g(4)=12, g'(4)=-1/5

400
Differentiate y=3tan√x
y′ =3sec²√(x)/ 2√x
400

Differentiate y=x2cos-1(2x)

y′ = 2xcos-1(2x) - (2x2)/sqrt(1-4x2)

400
Differentiate y= (x³lnx)/(x+2)
y′ = [x²(2xlnx+6lnx+x+2)]/ (x+2)²
400
d/dx arcsec(x)=
1/ |x| √(x² - 1)
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