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

Differentiate y=tan(6x)

y′ =6sec²(6x)

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(5x)sin(3x)

y′ =-5csc(5x)cot(5x)sin(3x) + 3cos(3x)csc(5x)

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^-x²cos2x

y′ =−2xe^(−x²) cos2x−2e^(−x²)sin2x

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 sin5(2x2 -1)

20xcos4(2x2 - 1)

500

Find the derivative of 3x4 - 5x2 + x - x-2

12x3 - 10x + 1 + 3x-3

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= (x³lnx)/(x+2)
y′ = [x²(2xlnx+6lnx+x+2)]/ (x+2)²
500

d/dx ln[(4/(x2 - 3x + 1))3]

(-6x + 9)/(x2 - 3x + 1)

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