Core 3 - Integrating and Differentiating functions

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Product rule
(dy/dx) = u(dv/dx) + v(du/dx)
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Quotient rule
(dy/dx) = [ v(du/dx) - u(dv/dx) ] / v^2
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Chain rule
(dy/dx) = (dy/du) x (du/dx)
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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
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Integration by parts
S[ u(dv/dx) ]dx = (uv) - S[ v(du/dx) ] dx :
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Other cards in this set

Card 2

Front

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

Back

Quotient rule

Card 3

Front

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

Back

Preview of the back of card 3

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

Back

Preview of the back of card 4

Card 5

Front

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

Back

Preview of the back of card 5

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