Test 2 Study

Question 1

d/dx (sin^-1)

Answer 1

1/sqrt(1-x^2)

Question 2

d/dx (tan^-1)

Answer 2

1/x^2 + 1

Question 3

lim as x-> infinity tan^-1(x)

Answer 3

pi/2

Question 4

lim as x-> -infinity tan^-1(x)

Answer 4

-pi/2

Question 5

d/dx (e^x)

Answer 5

d/dx (e^power) • d/dx (d/dx power)

Question 6

d/dx lnx

Answer 6

1/x

Question 7

d/dx b^x

Answer 7

(ln b) b^x

Question 8

d/dx ln(function)

Answer 8

1/function • d/dx (funtion)

Question 9

log (base b) x

Answer 9

ln x/ln b

Question 10

Steps to Log Differentiation:

Answer 10

1. Take ln of both sides and simplify
2. Differentiate with respect to x
3. Solve for y

Question 11

Steps for Implicit Differentiation:

Answer 11

1. Take d/dx of both sides

2. Solve for dy/dx

Question 12

Chain rule method 1

Answer 12

d/dx outside (inside) • d/dx outside

Question 13

Chain rule method 2

Answer 13

dy/dx = dy/du • du/dx
y = f(u) and u = g(x)

Question 14

d/dx a^power

Answer 14

d/dx a^power • d/dx power • ln a

Question 15

When do you use Logarithmic Differentiation?

Answer 15

d/dx funtion^function

Question 16

d/dx sinx

Answer 16

cosx

Question 17

d/dx cos

Answer 17

-sinx

Question 18

d/dx tanx

Answer 18

sec^2x

Question 19

d/dx cotx

Answer 19

-csc2x

Question 20

d/dx secx

Answer 20

secx tanx

Question 21

d/dx cscx

Answer 21

-cscx cotx