Basic Derivative Information and Power Rule
Chain Rule
Product Rule
Quotient Rule
Trig Derivatives
1
The derivative calculates the ________.
Slope
1
Define the Chain Rule for f(g(x))
g′(x)f′(g(x))
1
Define the Product Rule using f(x)g(x)
f′(x)g(x)+ g′(x)f(x)
1
Define the Quotient Rule using f(x)/g(x)
[g(x)f′(x) - f(x)g′(x)]/ (g(x))²
1
d/dx cosx=
-sinx
2
d/dx 5 =
0
2
d/dx (3x+1)²
6(3x+1)
2
f(x)=x²sinx, what is f′(x)?
2xsinx+ x²cosx
2
Differentiate y= 2/(x+1)
y′ = -2/ (x+1)²
2
Differentiate y=tan(x)
y′ =sec²(x)
3
d/dx x² =
2x
3
d/dx sin(4x²)
8xcos(4x²)
3
Differentiate y=x³lnx
y′ =x²(1+3lnx)
3
Differentiate y= (1+lnx) / (x²-lnx)
y′= [(1/x)-x-2xlnx] / (x²-lnx)²
3
Differentiate y=csc(x)
y′ =-csc(x)cot(x)
4
d/dx 3x²-x+3 =
6x-1
4
Differentiate y=√13x²-5x+8
y′ =26x-5/ 2√13x²-5x+8
4
Differentiate y=e^-x²cos2x
y′ =−2xe^(−x²) cos2x−2e^(−x²)sin2x
4
f(x)= (x²-1)³/ x²+1, what is f′(x)?
f′(x)= [4x(x²-1)²(x²+2)] / (x²+1)²
4
d/dx sin(2x)
2cos(2x)
5
Speed is _________.
the absolute value of velocity
5
Differentiate y=3tan√x
y′ =3sec²√(x)/ 2√x
5
Differentiate y=x²sin³(5x)
y′ =xsin²(5x)[15xcos(5x)+2sin(5x)]
5
Differentiate y= (x³lnx)/(x+2)
y′ = [x²(2xlnx+6lnx+x+2)]/ (x+2)²
5
d/dx arcsec(x)=
1/ |x| √(x² - 1)
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