Basic Derivative Information and Power Rule
Chain Rule
Product Rule
Quotient Rule
Trig Derivatives
100
The derivative calculates the ________.
Slope of the tangent line
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
18x+6
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=x³(ln4)^x
y′ =(3x² + ln4x³)(ln4^x)
300
Differentiate y= (1+e^x)^2 / x
y′= [(2xe^(2x)+2xe^x-e^(2x)-2e^x-1)/x²]
300
Differentiate y=[(sin(e^x)+cos(e^x))/((sinx)^2 +(cosx)^2)]
y′ = [e^x(cos(e^x)-sin(e^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
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(3x)cos(3x)
3(cos(3x))^2-3(sin(3x))^2)
500
f(a) - f(b) _________ = a - b
f'(c)
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= (x³cosx)/(x+2)
y′ = [3x²cosx(x+2)-x³sinx(x+2)-x³cosx]/ (x+2)²
500
d/dx csc(x) - sec(x)
y′ =-csc(x)cot(x)+sec(x)tan(x)
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