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5691277
Chain, Product, Qoutient
Description
A-Level Maths Mind Map on Chain, Product, Qoutient, created by uali34 on 08/06/2016.
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differentiation
maths core 3
maths
a-level
Mind Map by
uali34
, updated more than 1 year ago
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sammy414
over 10 years ago
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uali34
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Resource summary
Chain, Product, Qoutient
Chain rule
Use when a function of x
eg. y= (x^3 + 4)^7
y= du/dx x dy/dx
Method:
1. Find u ( inner most function) 2. Rewrite y in terms of u
3. Differentiate y with respect to u dy/du 4. Differentiate u with respect to x du/dx
5. Multiply the two together dy/dx 6. Replace u with the correct term
Product rule
Use when functions of x are multiplied together
eg. y= e^x x^8
y= u(dv/dx) + v(du/dx)
Method:
1. Find u and v ( two different functions) 2. Differentiate u with respect to x du/dx
3. Differentiate v with respect to x dv/dx 4. Replace the terms in dy/dx = udv+vdu
Qoutient rule
Use when functions of x are being divided
eg. y= x^3 +1 / 2x^2 +3
y= vdv- udv / v^2
Method:
1. Find u and v u=top function v=denominator 2.differntiate u with respect to x du/dx
3. Differentiate v with respect to x dv/dx 4. Replace the terms in dy/dx = vdu-udv/ v^2
How to differentiate :
Take the power to the front then decrease the power by one
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