Diffrentiation Rules

Question 1

Chain rule

Answer 1

Dy/dx = dy/du x du/dx

E.g.
y = (x^2 +4x) ^3

u= x^2 + 4x
y= u^3

Question 2

Product rule

Answer 2

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

E.g.
y= 5x(x+2)^3

u= 5x
v= (x+2)^3

Question 3

Quotient rule

Answer 3

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

E.g.
y= 2x / x+1

where u= 2x
v= x+1

Question 4

What does it mean if second derivative d^2y /dx^2 is positive?

Answer 4

Concave up

Gradient is increasing (getting more positive or less negative)

Question 5

What does it mean if second derivative is negative?

Answer 5

Concave down

The gradient is decreasing (getting less positive or more negative)

Question 6

Stationary points of inflection

Answer 6

• when second derivative=0

- concave up and concave down

Question 7

Non-stationary points of inflection

Answer 7

• Where dy/dx doesn’t equal 0

- Concave up and concave down

Question 8

How a maximum point is classified?

Answer 8

Second derivative is less than 0

Question 9

How minimum point is classified?

Answer 9

Second derivative is positive