# Core 3 - Integrating and Differentiating functions

Product rule
(dy/dx) = u(dv/dx) + v(du/dx)
1 of 5
Quotient rule
(dy/dx) = [ v(du/dx) - u(dv/dx) ] / v^2
2 of 5
Chain rule
(dy/dx) = (dy/du) x (du/dx)
3 of 5
Integration by substitution
Choose term for u : differentiate u : rearrange for [du = a(dx) ] : write original in terms of u and du : integrate and substitute x back in
4 of 5
Integration by parts
S[ u(dv/dx) ]dx = (uv) - S[ v(du/dx) ] dx :
5 of 5

## Other cards in this set

### Card 2

#### Front

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

Quotient rule

### Card 3

#### Front

(dy/dx) = (dy/du) x (du/dx)

### Card 4

#### Front

Choose term for u : differentiate u : rearrange for [du = a(dx) ] : write original in terms of u and du : integrate and substitute x back in

### Card 5

#### Front

S[ u(dv/dx) ]dx = (uv) - S[ v(du/dx) ] dx :

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