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(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=tan(x)

y′ =sec2x

400
d/dx 3x²-x+3 =
6x-1
400
Differentiate y=√13x²-5x+8
y′ =26x-5/ 2√13x²-5x+8
400

Differentiate y=2excosx

y′ =2excosx-2exsinx

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 csc(x)

csc(x)cot(x)

500

dy/dx means ______

The derivative of y with respect to x

500
Differentiate y=3tan√x
y′ =3sec²√(x)/ 2√x
500

Differentiate y=x²sec(x)

y′ =x2sec(x)tan(x)+2xsec(x)

500

Differentiate y= (x³lnx)/(x+2)

y′ = [x²(2xlnx+6lnx+x+2)]/ (x+2)²

500
d/dx arcsec(x)=
1/ |x| √(x² - 1)
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