Differentiation Chapter 9

Question 1

What does sin kx diff to

Answer 1

kcoskx

Question 2

What does nCoskx diff to

Answer 2

-knSinkx

Question 3

What does e x diff to

Answer 3

e x

Question 4

What does ae bx diff to

Answer 4

abe bx

Question 5

What does ae f(x) diff to

Answer 5

af’(x)e f(x)

Question 6

What does ak f(x) diff to

Answer 6

af’(x)k f(x) x lnk

Question 7

What does lnx diff to

Answer 7

1/x

Question 8

What does ln(f(x)) diff to

Answer 8

1/f(x) x f’(x)

Question 9

what does ax n diff to

Answer 9

nax (n-1)

Question 10

What does k(ax+b)n diff to

Answer 10

nk(ax+b)n-1 x a

Question 11

What does k( f(x) )n diff to

Answer 11

nk( f(x) )n-1 x f’(x)

Question 12

What can dy/dx be broken down into

Answer 12

dy/du x du/dx

Question 13

What is dy/dx x dx/dy equal to

Answer 13

1

Question 14

What is kSinn (mx) diff to

Answer 14

knSin(n-1) (mx) x mcos(mx)

Question 15

What does kCosn (mx) diff to

Answer 15

knCos(n-1) (mx) x -mSin(mx)

Question 16

What does f(x)g(x) diff to

Answer 16

f’(x)g(x) + f(x)g’(x)

Question 17

What does f(x) / g(x) diff to

Answer 17

f’(x)g(x) - f(x)g’(x) / (g(x))2

Question 18

What does tankx diff to

Answer 18

ksec2 kx
in formula book

Question 19

what does cotkx diff to

Answer 19

-kcosec2 kx
in formula book

Question 20

what does coseckx diff to

Answer 20

-kcoseckxcotkx
in formula book

Question 21

what does seckx diff to

Answer 21

kseckxtankx
in formula book

Question 22

What equation do you use for parametric equations

Answer 22

dy/dx = dy/dt x dt/dx

Question 23

What does it mean when f’‘(x) is bigger than 0

Answer 23

f(x) is convex

Question 24

What does it mean when f’‘(x) is less than 0

Answer 24

f(x) is concave

Question 25

What does it mean when f’‘(x) =0

Answer 25

point of inflexion

Question 26

How do you find points of inflexion

Answer 26

solve f’‘(x) = 0

Question 27

How do you prove a point is a point of inflexion

Answer 27

show that f’‘(x) changes sign close to your point