Basic Derivative Information and Power Rule
Chain Rule
Product Rule
Quotient Rule
Trig Derivatives +Chain Rule
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 cos(2x)=

-2sin(2x)

200
d/dx 5 =
0
200

d/dx (e7x^2)

14xe7x^2
200
f(x)=x²sinx, what is f′(x)?
2xsinx+ x²cosx
200
Differentiate y= 2/(x+1)
y′ = -2/ (x+1)²
200

Differentiate y=tan3(x)

y′ =3tan2(x)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(cos(x))

y′ =csc(cos(x))cot(cos(x))sin(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^-x²cos2x

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(e7x)

7e7xcos(e7x)

500

What does the Intermediate Value Theorem state?

If f(x) is continuous on the interval [a,b], then there exists a c in the interval such that f(a) < f(c)< f(b).

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(5x)=

5/ |x| √(x² - 1)

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