P3 and P4 Differentiation

Question 1

differentiate sinkx

Answer 1

k cos kx

Question 2

differentiate coskx

Answer 2

-k sin kx

Question 3

differentiate e to the power kx

Answer 3

ke to the power kx

Question 4

differentiate ln x

Answer 4

1 / x

- use product rule for other lns

Question 5

Chain rule

Answer 5

allows you to differentiate when you have a composite function (function inside a function)

e.g. y = (3x^4 + x)^5
dy/dx = 5(3x^4 + x)^4 times 12x^3 + 1
- times the power of the bracket to the front
- subtract one from the power
- times the whole thing with differentiated of inside the brackets

Question 6

dx/dy =

Answer 6

1 / (dy/dx)

Question 7

Product rule

Answer 7

If y = uv

then dy/dx = vu’ (differentiated u) + uv’ (differentiated v)

Question 8

Quotient rule

Answer 8

If y = uv

then dy/dx = vu’ - uv’ / v^2

Question 9

differentiate tan(x)

Answer 9

sec^2(x)

Question 10

differentiate cosec(x)

Answer 10

• cosec(x) cot(x)

Question 11

differentiate sec(x)

Answer 11

sec(x) tan(x)

Question 12

differentiate cot(x)

Answer 12

• cosec^2(x)

Question 13

differentiating parametric equations

Answer 13

chain rule

dy/dx = dy/du x du/dx

Question 14

differentiating implicit functions using chain rule

Answer 14

d/dx (y^n) = n y^(n-1) dy/dx

Question 15

differentiating implicit functions using product rule

Answer 15

d/dx (xy) = x dy/dx + y

Question 16

differentiate a^x

Answer 16

if y = a^x

then dy/dx = a^x lna

Question 17

meaning of dy/dx

Answer 17

change in the rate of y in respect to x

Question 18

If dN/dt proportional to N with an increasing constant…

Answer 18

dN/dt = kN

Question 19

If dN/dt proportional to N with a decreasing constant…

Answer 19

dN/dt = - kN