Ch 5 Sec 4 5 And Ch 6 Sec 2

Question 0

D
—- a^u
Dx

Answer 0

( lna ) a^u du/dx

Question 1

D
—- a^x
Dx

Answer 1

( lna ) a^x

Question 2

D
—- [log. x]
Dx. a

Answer 2

( lna ) x

Question 3

D
—- [ log. u]
Dx. a

Answer 3

1. Du
   ——— —-
   ( lna ) u. Dx

Question 4

In exponential growth the rate of growth is constant

Answer 4

False

Question 5

In linear growth the rate of growth is constant

Answer 5

True

Question 6

The differential equation modeling exponential growth is dy/dx = key where k is constant

Answer 6

True

Question 7

Steps to solve a separation of variables

Answer 7

Put same variables on same side
Anti-differentiate in terms of that variable
Keep in mind to change see when manipulating
Remember the absolute value disappears because of the exponential

Question 8

What is the implicit form

Answer 8

When you leave the x and y variables equal to c

Question 9

When do you solve for y during separation of variables

Answer 9

If you exponentiation or use the natural log

Question 10

What is the change of base formula

Answer 10

lnx
Log x = ——
a lna

Question 11

How do you differentiate functions raised to functions

Answer 11

Take the natural log both sides

Implicit differentiation

Make it in terms of X

Question 12

Find derivative

y = a^x

Answer 12

y’= a^x lna

Question 13

Find derivative

   y= a^u

Answer 13

y’ = a^u (lna) u’

Question 14

What does it mean when log functions have a restricted domain

Answer 14

Can’t use negative numbers