Chapter 5: Exponential, Logs, Derivatives of Inv. Trigs

Question 1

a^x =

Answer 1

e^x*lna

Question 2

d/dx a^x

Answer 2

a^x ln(a)

Question 3

Integral of a^x dx

Answer 3

a^x/ln(a) + C

Question 4

Express the following logarithm in terms of the natural logarithm.

log_ax

Answer 4

ln(x)/ln(a)

Question 5

d/dx (log_ax)

Answer 5

1/(x*ln(a))

Question 6

d/dx (arcsin x)

Answer 6

1/sqrt(1-x²)

Question 7

d/dx (arccos x)

Answer 7

-1/sqrt(1-x²)

Question 8

d/dx (arctan x)

Answer 8

1/(1+x²)

Question 9

d/dx (arccsc x)

Answer 9

-1/(x*sqrt(x²-1))

Question 10

d/dx (arcsec x)

Answer 10

1/(x*sqrt(x²-1))

Question 11

d/dx (arccot x)

Answer 11

-1/(1+x²)