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)
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 x² =
2x
300
d/dx sin(4x²)
8xcos(4x²)
300
Differentiate y=x³lnx
y′ =x²(1+3lnx)
300
Differentiate y= (1+lnx) / (x²-lnx)
y′= [(1/x)-x-2xlnx] / (x²-lnx)²
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^-x²)(cos2x)

y′ =−2x(e^−x²) cos2x−2(e^−x²)sin2x

400

Differentiate f(x)= (2-5x)/(3x2-5)

f′(x)=(15x2-12x+25)/(3x2-5)2

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

Differentiate y= 2x/√(3-4x3)

y′ = [2√(3-4x3) +(6x2(3-4x3)-1/2)(2x)]/

√(3-4x3)2

500

d/dx sin(x2tanx)

cosx(x2tanx)(2xtanx+x2sec2x)

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