Math 131 - Exam 2

e^x

e^x

a^x

a^x ln(a)

Product Rule [f(x)g(x)]

f'(x)g(x) + f(x)g'(x)

Quotient Rule [f(x)/g(x)]

f'(x)g(x) - f(x)g'(x) / g(x)^2

sin(x)

cos(x)

cos(x)

-sin(x)

tan(x)

sec^2(x)

csc(x)

-csc(x)cot(x)

sec(x)

sec(x)tan(x)

cot(x)

-csc^2(x)

Chain Rule f(g(x))

f'(g(x)) g'(x)

e^0

1

If e is raised to more than just x

chain rule it

ln(x)

1/x

logb(x)

1/ln(b)x

ln|x|

1/x

logb|x|

1/ln(b)x

arctan(x) (tan^-1(x))

1/1+x^2

arcsin(x) (sin^-1(x))

1/sqrt(1-x^2)

Speeding Up

Velocity and acceleration same signs

Slowing Down

velocity and acceleration different signs

Velocity

s'(t)

Acceleration

s"(t)

At Rest

v(t) = 0

Moving Right

velocity is positive (above x-axis)

Moving Left

velocity is negative (below x-axis)

e^x will...

never equal 0

Finding Total Distance

use original equation s(t)

Exponential Growth and Decay Equation

P(t) = Poe^kt

Linearizations

L(x) = f(a) + f'(a)(x-a)