P2 Calculus

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

Differentiate a^(kx)

Answer 5

(a^(kx))(k)(ln(a))

Question 6

What is the chain rule?

Answer 6

dy/dx = (dy/du) × (du/dx)

Question 7

How to get from dx/dy to dy/dx?

Answer 7

dy/dx = 1 / (dx/dy)

Question 8

What is the product rule?

Answer 8

If y = uv, then dy/dx = u(dv/dx) + v(du/dx)

Question 9

What is the quotient rule?

Answer 9

If y = u/v, then dy/dx = (v(du/dx) - u(dv/dx)) / v²

Question 10

Differentiate tan(kx)

Answer 10

k sec²(kx)

Question 11

Differentiate cosec(kx)

Answer 11

-k cosec(kx) cot(kx)

Question 12

Differentiate sec(kx)

Answer 12

k sec(kx) tan(kx)

Question 13

Differentiate cot(kx)

Answer 13

-k cosec²(kx)

Question 14

For parametric functions, how do you get dy/dx?

Answer 14

(dy/dt) / (dx/dt)

Question 15

How to do implicit differentiation?

Answer 15

Differentiate y like x, then multiply it by dy/dx

Question 16

f(x) is concave if f’‘(x) is what?

Answer 16

≤ 0

Question 17

f(x) is convex if f’‘(x) is what?

Answer 17

≥ 0

Question 18

What is the point called where a curve changes from concave to convex or vice versa?

Answer 18

The point of inflection

Question 19

How is the point of inflection seen mathematically?

Answer 19

f’‘(x) changes signs

Question 20

Integration of x^n

Answer 20

(x^(n+1)) / (n+1)

Question 21

Integration of e^x

Answer 21

e^x

Question 22

Integration of 1/x

Answer 22

ln(x)

Question 23

Integration of cos(x)

Answer 23

sin(x)

Question 24

Integration of sin(x)

Answer 24

-cos(x)

Question 25

Integration of sec²(x)

Answer 25

tan(x)

Question 26

Integration of cosec(x)cot(x)

Answer 26

-cosec(x)

Question 27

Integration of cosec²(x)

Answer 27

-cot(x)

Question 28

Integration of sec(x)tan(x)

Answer 28

sec(x)

Question 29

Integration of f'(ax + b)

Answer 29

(1/a) * f(ax + b)

Question 30

Formula for integration by parts

Answer 30

∫u * (dv/dx) = uv - ∫v * (du/dx)

Question 31

Trapezium rule formula

Answer 31

∫y between a and b = (h/2)(y₀ + 2(y₁ + y₂ + y₃ … + Yn₋₁) + yn)

Question 32

When dy/dx = f(x)g(y), how can this be rewritten?

Answer 32

∫(1/g(y)) = ∫f(x)

Question 33

Integration of the limit of a sum for the integration of f(x) between a and b

Answer 33

limit of dx → 0 for ∑f(x) when x = a and b on the top