Differentiation

Question 1

Meaning of f’(x)<0

Answer 1

decreasing function

Question 2

Meaning of f’(x)=0

Answer 2

stationary function

Question 4

Meaning of f’(x)>0

Answer 4

increasing function

Question 5

Meaning of f’‘(x)<0

Answer 5

Concave
Maximum

Question 6

Meaning of f’‘(x)=0

Answer 6

point of inflection

Question 7

Meaning of f’‘(x)>0

Answer 7

Convex
Minimum

Question 9

Differentiate axⁿ

Answer 9

an x^n-1

Question 9

Differentiate a^x

Answer 9

lna a^x

Question 10

Differentiate e^x

Answer 10

e^x

Question 11

Differentiate e^3x

Answer 11

3e^3x

Question 12

Differentiate lnx

Answer 12

1/x

Question 13

Differentiate sinx

Answer 13

cosx

Question 14

Differentiate cosx

Answer 14

-sinx

Question 15

Differentiate tanx (FB)

Answer 15

sec²x

Question 16

Differentiate secx (FB)

Answer 16

secx tanx

Question 16

Differentiate cotx (FB)

Answer 16

-cosec²x

Question 17

Differentiate cosecx (FB)

Answer 17

-cosecxcotx

Question 18

Product rule: f(x)g(x)

Answer 18

f’(x)g(x) + f(x)g’(x)

Question 19

Implicit Diff: f(y) =

Answer 19

f’(y) * dy/dx

Question 20

Chain rule: f(…..) =

Answer 20

f’(…..) * (…..)’

Question 21

Reciprocal =

Answer 21

1/gradient or dx/dy

Question 22

Parametric Differentiation

Answer 22

(dy/dx) = (dy/dt) x (dt/dx)

Question 23

Connected rates of change differentiation

Answer 23

(dV/dt) = (dV/…) x (…/dt)

causes other variable to cancel

Question 24

Rate is ….

Answer 24

(…)/dt