Chain, Product, Qoutient

sammy414
Mind Map by , created almost 6 years ago

Maths core 3 (Differentiation) Mind Map on Chain, Product, Qoutient, created by sammy414 on 12/04/2013.

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sammy414
Created by sammy414 almost 6 years ago
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Chain, Product, Qoutient
1 Chain rule
1.1 Use when a function of x
1.1.1 eg. y= (x^3 + 4)^7
1.1.2 y= du/dx x dy/dx
1.2 Method:
1.2.1 1. Find u ( inner most function) 2. Rewrite y in terms of u
1.2.1.1 3. Differentiate y with respect to u dy/du 4. Differentiate u with respect to x du/dx
1.2.1.1.1 5. Multiply the two together dy/dx 6. Replace u with the correct term
2 Product rule
2.1 Use when functions of x are multiplied together
2.1.1 eg. y= e^x x^8
2.1.2 y= u(dv/dx) + v(du/dx)
2.1.3 Method:
2.1.3.1 1. Find u and v ( two different functions) 2. Differentiate u with respect to x du/dx
2.1.3.1.1 3. Differentiate v with respect to x dv/dx 4. Replace the terms in dy/dx = udv+vdu
3 Qoutient rule
3.1 Use when functions of x are being divided
3.1.1 eg. y= x^3 +1 / 2x^2 +3
3.1.2 y= vdv- udv / v^2
3.1.3 Method:
3.1.3.1 1. Find u and v u=top function v=denominator 2.differntiate u with respect to x du/dx
3.1.3.1.1 3. Differentiate v with respect to x dv/dx 4. Replace the terms in dy/dx = vdu-udv/ v^2
4 How to differentiate :
4.1 Take the power to the front then decrease the power by one

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