Unit 3 - Derivative rules

Question 1

d/dx (x^n)

Answer 1

d/dx= nx^n-1

Question 2

d/dx (k * f(x))

Answer 2

d/dx= k * f’(x)

Question 3

d/dx (f(x) ± g(x))

Answer 3

d/dx= f’(x) ± g’(x)

Question 4

d/dx (e^u)

Answer 4

d/dx= e^u * du

Question 5

d/dx (a^u)

Answer 5

d/dx= a^u * ln(a) *du

Question 6

d/dx (u * v)

Answer 6

d/dx= (u)(dv) + (v)(du)

Question 7

d/dx= Hi/Lo

Answer 7

d/dx= ((Lo)(dHi) - (Hi)(dLo)) / LoLo

Question 8

d/dx (sinx)

Answer 8

d/dx= cosx

Question 9

d/dx (cosx)

Answer 9

d/dx= -sinx

Question 10

d/dx (tanx)

Answer 10

d/dx= (secx)^2

Question 11

d/dx (cscx)

Answer 11

d/dx= -cscx * cotx

Question 12

d/dx (secx)

Answer 12

d/dx= secx * tanx

Question 13

d/dx (cotx)

Answer 13

d/dx= -csc^2x

Question 14

Composition: What is another way to write (f o g)(x)

Answer 14

f(g(x))

Question 14

d/dx(f(u)) <– chain rule

Answer 14

d/dx= f’(u) * du

Question 15

d/dx (ln(u))

Answer 15

d/dx= 1/u * du

Question 16

d/dx (loga(u))

Answer 16

d/dx= (1/u*ln(a)) *du

Question 17

d/dx (sin-1u)

Answer 17

d/dx = (1/√1-u^2) * du

Question 18

d/dx (cos-1u)

Answer 18

d/dx = -(1/√1-u^2) * du

Question 19

d/dx (tan-1u)

Answer 19

d/dx = (1/1+u^2) * du

Question 20

d/dx (cot-1u)

Answer 20

d/dx = -(1/1+u^2) * du

Question 21

d/dx (sec-1u)

Answer 21

d/dx = (1/IuI * √u^2-1) * du

Question 22

d/dx (csc-1u)

Answer 22

d/dx = -(1/IuI * √u^2-1) * du

Question 23

(f-1)’(b)

Answer 23

= 1/f’(a)