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Basic Derivative Information and Power Rule
Chain Rule
Product Rule
Quotient Rule
Trig Derivatives
100

The derivative calculates the ________.

Slope of the tangent line

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)

or

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)=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 1/√(x)

-1/2 x-3/2

300
d/dx sin(4x²)
8xcos(4x²)
300

Differentiate y=x³cosx

y′ =x3(-sinx)+cosx(3x2)

300

Differentiate y= (1+cotx) / (x²-2x)

y′= [(x²-2x)(-csc2x)-(1+cotx)(2x-2)]/(x²-2x)2

300
Differentiate y=csc(x)
y′ =-csc(x)cot(x)
400

d/dx 1/x - 1/x3 =

-x-2 + 3x-4

400

Differentiate y=(2x-5)-2(x2-4x)6

y′ =2(x2-4x)5(2x-5)-3(10x2-46x+60)

400

Differentiate y=x5cos2x

y′ =x5(-sin2x)(2) + cos2x (5x4)

400
f(x)= (x²-1)³/ x²+1, what is f′(x)?
f′(x)= [4x(x²-1)²(x²+2)] / (x²+1)²
400
d/dx sin(2x)
2cos(2x)
500

The rate of change of position is

velocity

500
Differentiate y=3tan√x
y′ =3sec²√(x)/ 2√x
500
Differentiate y=x²sin³(5x)
y′ =xsin²(5x)[15xcos(5x)+2sin(5x)]
500

Differentiate y= (x³sinx)/(x+2)

y′ = (x3cosx)(x+2)+(2x2sinx)(x+3)/(x+2)2

500

d/dx secx=

y'=secxtanx