Calculus Chapter 6: Inverse Functions

Question 1

a^x in terms of e and ln

Answer 1

e^{x lna}

Question 2

Derivative of a^x

Answer 2

a^x lna

Question 3

Integral of a^x

Answer 3

a^x/ lna + C where a != 1

Question 4

Derivative of log_ax

Answer 4

¹/_{x lna}

Question 5

Number e as a limit

Answer 5

limit as x->0 (1+x)^1/x

Question 6

Derivative of sin^-1x

Question 7

Cancellation equations for cos

Answer 7

cos^-1 (cos x) = x

_{for x E [0,π]}

Question 8

Derivative of cos^-1x

Question 9

Derivative of tan^-1x

Answer 9

( 1 + x²)^-1

Answer 10

sin^-1x + C

Question 11

Integral of (x² + 1 )^-1

Answer 11

tan^-1x + C

Question 12

Integral of

(x² + a²) ^{<strong>-1</strong>}

Answer 12

¹/_a tan^-1(^x/_a) + C