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 2y=x³
y′ =3(x^2)/2
300
Differentiate y= (x^2)/(x-1)
y′= ((x^2)-2x)/(x-1)^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=x²cos2x
y′ =2xCos(2x) + 2(x^2)Sin(2x)
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 sin(2x)
2cos(2x)
500
The second derivative of the position function s(t) is ________.
acceleration
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= (x³)/(x+2)
y′ = ((3(x^2)+6x-(x^3))/(x+2)^2
500
d/dx tan(x)cos(x)
= Sec^2(x)Cos(x) - (Sin^2(x))/cos(x)
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