Differentiation

Question 1

Constant Rule d(c)

Answer 1

0

Question 2

Sum/Difference Rule d(f +/- g)

Answer 2

(f ‘) +/- (g ‘)

Question 3

Product Rule d(fg)

Answer 3

f(g ‘) + g(f ‘)

Question 4

Quotient Rule d(f/g)

Answer 4

[g(f ‘) - f(g ‘)]/ g^2

Question 5

Constant Multiple Rule d(cf)

Answer 5

c(f ‘)

Question 6

Power Rule d(x^n)/d(x)

Answer 6

nx^(n-1)/ 1

Question 7

d(sin(x))

Answer 7

cos(x)

Question 8

d(cos(x))

Answer 8

-sin(x)

Question 9

d(tan(x))

Answer 9

sec^2(x)

Question 10

d(sec(x))

Answer 10

sec(x)tan(x)

Question 11

d(csc(x))

Answer 11

-csc(x)cot(x)

Question 12

d(cot(x))

Answer 12

-csc^2(x)

Question 13

Chain Rule d[f(u)]

Answer 13

f ‘(u) x u ‘ or f ‘(g(x)) x g ‘(x)

Question 14

What is similar to Chain Rule?

Answer 14

Order of Operations

Question 15

General Power Rule d[u^n]

Answer 15

nu^(n-1) x u ‘

Question 16

What is a Derivative?

Answer 16

Slope or Rate of Change

Question 17

Physics

Answer 17

Veloc= Posit ‘, Accel=Veloc ‘, Accel=Posit ‘’

Question 18

Velocity

Answer 18

(Position(x)-Position(y))/(Time(x)-Time(y))

Question 19

Acceleration

Answer 19

(Velocity(x)-Velocity(y))/(Time(x)-Time(y))

Question 20

Limit Definition

Answer 20

[f(x+h)-f(x)]/h

Question 21

If f is differentiable at x=c

Answer 21

f is continuous at x=c

Question 22

No Derivative #1

Answer 22

Discontinuity

Question 23

No Derivative #2

Answer 23

Absolute Value or Sharp Turn (or “Will” function that is W-shaped)

Question 24

No Derivative #3

Answer 24

Square Root

Question 25

No Derivative #4

Answer 25

VTL (Vertical Tangent Line)