Basic Derivative Information and Power Rule
Normal/Tangent Lines
Product Rule
Quotient Rule
Trig Derivatives
100

The derivative calculates the ________.

Slope

100

The slope of the tangent line of f(x).

What is f′(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 sin x=

cos x

200

d/dx 5 =

0

200

The slope of the normal line of f(x).

What is -1/f'(x)?

200
f(x)=x²sinx, what is f′(x)?
2xsinx+ x²cosx
200
Differentiate y= 2/(x+1)
y′ = -2/ (x+1)²
200

Differentiate y=cos(x)

y′ =-sin(x)

300

d/dx x² =

2x

300

The equation, in point-slope form, of the line tangent to y=x4 -x3 +2 at the point (2, -6).

What is y+6=20(x-2)?

300

Differentiate y=x³*sin(x)

y′ =x3*cos(x) + sin(x)*3x2

300

Differentiate y= (1+ x) /x²

y′= [x2-(1+x)*2x] / x4

300

Differentiate y=csc(x)

y′ =-csc(x)cot(x)

400

d/dx 3x²-x+3 =

6x-1

400

The equation, in point-slope form, of the line tangent to y=x / x-1 at the point (3, 1.5).

What is y-1.5= -1/4 (x-3)?

400

Differentiate y=x²cot(x)

y′ =-x2csc2x +2x*cot(x)

or

y′ = 2x*cot(x)-x2csc2x

400

f(x)= (x²-1)/ (x²+1), what is f′(x)?

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

400

d/dx sec(x)

sec(x)tan(x)

500

d/dx 2(x3 - 2x + 4)

6x2-4

500

The equation, in point-slope form, of the normal line for y=x / x-1 at the point (3, 1.5).

What is y-1.5=4 (x-3)?

500

Differentiate y=2x sin(x) + x3 cos(x)

y′ =sin(x)*2 + 2x cos(x) -x3sin(x) +3x2cos(x)

500

Differentiate y= (x³)/(x+2)

y′ = [(x+2)*3x²-(x3)]/ (x+2)²

500

d/dx tan(x)

sec2(x)

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