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= 32x / (x²-lnx)

y′= [(x²-lnx)(2ln3•32x)–32x(2x–1/x)] / (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

f(x)= (x²-1)³ / x²+1, what is f′(x)?

f′(x)= [(x²+1)•6x(x²-1)2–2x(x²-1)³] / (x²+1)²

400

d/dx arcsec(x)=

1 / |x| √(x² - 1)

500

d/dx log(x)

1 / x ln(10)

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′ = [(x+2)(3x2lnx+x2)–x³lnx] / (x+2)²

500

d/dx arccot(2x)

-2 / 4x2+1

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