416848
Chain, Product, Qoutient
- Chain rule
- Use when a function of x
- eg. y= (x^3 + 4)^7
- y= du/dx x dy/dx
- eg. y= (x^3 + 4)^7
- 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
- 5. Multiply the two together dy/dx
6. Replace u with the correct term
- 3. Differentiate y with respect to u dy/du
4. Differentiate u with respect to x du/dx
- 1. Find u ( inner most function)
2. Rewrite y in terms of u
- Use when a function of x
- 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
- 3. Differentiate v with respect to x dv/dx
4. Replace the terms in dy/dx = udv+vdu
- 1. Find u and v ( two different functions)
2. Differentiate u with respect to x du/dx
- eg. y= e^x x^8
- Use when functions of
x are multiplied
together
- 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
- 3. Differentiate v with respect to x dv/dx
4. Replace the terms in dy/dx = vdu-udv/
v^2
- 1. Find u and v u=top function v=denominator
2.differntiate u with respect to x du/dx
- eg. y= x^3 +1 / 2x^2 +3
- Use when
functions of x are
being divided
- How to differentiate :
- Take the
power to the
front then
decrease
the power by
one
- Take the
power to the
front then
decrease
the power by
one
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