Show:
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 -3 =

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′ =−2xe^(−x²) cos2x−2e^(−x²)sin2x

400

Daily Double

f(x)= (x²-1)³/ x²+1, what is f′(x)?


f′(x)= [6x(x²-1)²(x²+1)2]/(x2+1)-[2x(x-1)3(x+1)3] / (x²+1)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= (x³lnx)/(x+2)
y′ = [x²(2xlnx+6lnx+x+2)]/ (x+2)²
500
d/dx arcsec(x)=
1/ |x| √(x² - 1)