unit 5 p 2

Question 1

d/dx [a^x]

Answer 1

a^x lna

Question 2

d/dx [loga x]

Answer 2

1/xlna

Question 3

∫ a^x dx

Answer 3

a^x/ln a +c

Question 4

d/dx e^x

Answer 4

e^x

Question 5

Derivatives of inverse trig functions

Answer 5

arcsin= u’/root 1-u^2
arccos= -u’/root 1-u^2

arctan= u’/1+u^2
arccot= -u’/1+u^2

arcsec= u’/|u|root u^2-1
arccsc= -u’/|u|root u^2-1

Question 6

∫ inverse trig functions

Answer 6

∫ du/root a^2-u^2 = arcsin u/a +c
∫ du/ a^2+u^2= 1/a arctan u/a +c
∫ du/ u root u^2-a^2= 1/a arcsec |u|/a +c