5a Differentiation

Question 1

xⁿ

Answer 1

n x^n-1

Question 2

[f(x)]ⁿ

Chain Rule

Answer 2

n [f(x)]^n-1 f’(x)

Question 3

f(x)g(x)

Product Rule

Answer 3

f’(x)g(x) + f(x)g’(x)

Question 4

f(x)/ g(x)

Quotient Rule

Answer 4

[f’(x)g(x) - f(x)g’(x)]/ g²(x)

Question 5

dx/dy

Answer 5

1/ (dy/dx)

Question 6

e^x

Answer 6

e^x

Question 7

e^f(x)

Answer 7

e^f(x) f’(x)

Question 8

ln x

Answer 8

1/x

Question 9

ln[(f(x)], f(x) > 0

Answer 9

[1/f(x)] f’(x) = f’(x)/ f(x)

Question 10

sin x

Answer 10

cos x

Question 11

sin[f(x)]

Answer 11

cos[f(x)] f’(x)

Question 12

sinⁿ[f(x)]

Answer 12

n [sin(f(x))]^n-1 [cos f(x)] f’(x)

Question 13

cos x

Answer 13

-sin x

Question 14

cos[f(x)]

Answer 14

-sin[f(x)] f’(x)

Question 15

cosⁿ[f(x)]

Answer 15

n [cos(f(x))]^n-1 [-sin f(x)] f’(x)

Question 16

tan x

Answer 16

sec²x

Question 17

tan[f(x)]

Answer 17

sec²[f(x)] f’(x)

Question 18

tanⁿ[f(x)]

Answer 18

n [tan(f(x))]^n-1 [sec² f(x)] f’(x)

Question 19

cotan x

Answer 19

-cosec²(x)

Question 20

cotan[f(x)]

Answer 20

-cosec²[f(x)] f’(x)

Question 21

Implicit Differentiation

Answer 21

• Apply Chain Rule to every term especially if differentiating y!
• Look out for Product Rule!

Question 22

Parametric Equation

Answer 22

1. Find Cartesian Equation by making t the subject in either equation and doing substitution.
2. Find dy/dx using Rate of Change equation.