Year 2 - Differentiation (Chapter 9)

Question 1

differentiate : sin(kx)

Answer 1

k cos kx

Question 2

differentiate : cos kx

Answer 2

• k sin kx

Question 3

differentiate : e^kx

Answer 3

k e^kx

Question 4

differentiate : ln x

Answer 4

1/x

Question 5

y = a^kx (a>0, k is real)

Answer 5

a^kx (ln a )

Question 6

chain rule:

Answer 6

dy/dx = dy/du * du/dx

Question 7

product rule for differentiating (y = uv)

Answer 7

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

Question 8

quotient rule for differentiating: y = u/v

Answer 8

dy/dx = v(du/dx) - u(dv/dx)
—————————-
v^2

Question 9

differentiate y = tan kx

Answer 9

k sec^2 kx

Question 10

differentiate y = cosec kx

Answer 10

• k cosec kx cot kx

Question 11

differentiate y = sec kx

Answer 11

• k sec kx tan kx

Question 12

differentiate : y = cot kx

Answer 12

• k cosec^2 kx

Question 13

differentiate : y = arcsin x

Answer 13

1 / sqrt(1-x^2)

Question 14

differentiate : y = arccos x

Answer 14

• 1/sqrt(1-x^2)

Question 15

differentiate : y = arctan x

Answer 15

1 / (1 + x^2)

Question 16

what is the eq. for parametric differentiation

Answer 16

dy/dx = dy/dt ÷ dx/dt

Question 17

when is a curve concave

Answer 17

f’‘(x) ≤ 0

Question 18

When is a curve convex

Answer 18

f’‘(x) ≥ 0

Question 19

what is a point of inflection

Answer 19

f’‘(x) = 0, change of sign on each sign