MIDTERM - Calc

Question 0

Power Rule: d/dx (u^n)

Answer 0

nu^(n-1)(du/dx)

Question 1

Derivative of a constant

Answer 1

f’(x)=0 when f(x)=c

Question 2

Constant Multiple Rule: d/dx(cf(x))

Answer 2

c(f’)

Question 3

Sum/Difference Rule: d/dx(f(x)±g(x))

Answer 3

f’+g’ [or] f’-g’

Question 4

Product Rule: d/dx[f(x)g(x)]

Answer 4

f(g’)+g(f’)

Question 5

Quotient Rule: d/dx[f(x)/g(x)]

Answer 5

(g(f’)-f(g’))/g^2

Question 6

d/dx(sinu)

Answer 6

cos(u)du/dx

Question 7

d/dx(cosu)

Answer 7

-sin(u)du/dx

Question 8

d/dx(tanu)

Answer 8

sec^2(u)du/dx

Question 9

d/dx(cotu)

Answer 9

-csc^2(u)du/dx

Question 10

d/dx(secu)

Answer 10

(secu)(tanu)du/dx

Question 11

d/dx(cscu)

Answer 11

-(cscu)(cotu)du/dx

Question 12

d/dx(lnu)

Answer 12

(1/u)(du/dx)

Question 13

d/dx(logbu)

Answer 13

(1/ulnb)(du/dx)

Question 14

d/dx(b^u)

Answer 14

b^u(lnb)(du/dx)

Question 15

d/dx(e^u)

Answer 15

e^u(du/dx)

Question 16

d/dx(sin^-1u)

Answer 16

(du/dx)/(√1-u^2)

Question 17

d/dx(cos^-1u)

Answer 17

-(du/dx)/(√1-u^2)

Question 18

d/dx(tan^-1u)

Answer 18

(du/dx)/(1+u^2)

Question 19

d/dx(cot^-1u)

Answer 19

-(du/dx)/(1+u^2)

Question 20

d/dx(sec^-1u)

Answer 20

(du/dx)/(u√u^2-1)

Question 21

d/dx(csc^-1u)

Answer 21

-(du/dx)/(u√u^2-1)