Calculus 1 – Derivatives
Calculus 1 – Derivatives

x2
b) Hence find; 1 x 3
dx
x2 2 3x 2
1 x 3
dx
3 2 1 x 3
dx
2
1 x3 c
3

x2
b) Hence find; 1 x 3
dx
x2 2 3x 2
1 x 3
dx
3 2 1 x 3
dx
2
1 x3 c
3
ii x 2 x 2 dx

x2
b) Hence find; 1 x 3
dx
x2 2 3x 2
1 x 3
dx
3 2 1 x 3
dx
2
1 x3 c
3
ii x 2 x 2 dx
1
2 x 2 x 2 dx
2

x2
b) Hence find; 1 x 3
dx
x2 2 3x 2
1 x 3
dx
3 2 1 x 3
dx
2
1 x3 c
3
ii x 2 x 2 dx
1
2 x 2 x 2 dx
2
2 x 2 2 c
3
1 2
2 3

x2
b) Hence find; 1 x 3
dx
x2 2 3x 2
1 x 3
dx
3 2 1 x 3
dx
2
1 x3 c
3
ii x 2 x 2 dx
1
2 x 2 x 2 dx
2
2 x 2 2 c
3
1 2
2 3
2 x 2 2 x 2 c
1
3

x2
b) Hence find; 1 x 3
dx
x2 2 3x 2
1 x 3
dx
3 2 1 x 3
dx
2
1 x3 c
3
ii x 2 x 2 dx OR x 2 x 2 dx
1
2 x 2 x 2 dx
2
2 x 2 2 c
3
1 2
2 3
2 x 2 2 x 2 c
1
3

x2
b) Hence find; 1 x 3
dx
x2 2 3x 2
1 x 3
dx
3 2 1 x 3
dx
2
1 x3 c
3
ii x 2 x 2 dx OR x 2 x 2 dx u 2 x2
1
2 x 2 x 2 dx
2
2 x 2 2 c
3
1 2
2 3
2 x 2 2 x 2 c
1
3

x2
b) Hence find; 1 x 3
dx
x2 2 3x 2
1 x 3
dx
3 2 1 x 3
dx
2
1 x3 c
3
ii x 2 x 2 dx OR x 2 x 2 dx u 2 x2
1 du
2 x 2 x 2 dx 2x
2 dx
du 2 xdx
2 x 2 2 c
3
1 2
2 3
2 x 2 2 x 2 c
1
3

x2
b) Hence find; 1 x 3
dx
x2 2 3x 2
1 x 3
dx
3 2 1 x 3
dx
2
1 x3 c
3
ii x 2 x 2 dx OR x 2 x 2 dx u 2 x2
1 du
2 x 2 x 2 dx u 2x
2 dx
du 2 xdx
2 x 2 2 c
3
1 2
2 3
2 x 2 2 x 2 c
1
3

x2
b) Hence find; 1 x 3
dx
x2 2 3x 2
1 x 3
dx
3 2 1 x 3
dx
2
1 x3 c
3
ii x 2 x 2 dx OR x 2 x 2 dx u 2 x2
1 du
2 x 2 x 2 dx 1 u 2x
2 du dx
2
du 2 xdx
2 x 2 2 c
3
1 2
2 3
2 x 2 2 x 2 c
1
3

x2
b) Hence find; 1 x 3
dx
x2 2 3x 2
1 x 3
dx
3 2 1 x 3
dx
2
1 x3 c
3
ii x 2 x 2 dx OR x 2 x 2 dx u 2 x2
1 du
2 x 2 x 2 dx 1 u 2x
2 du dx
2
du 2 xdx
2 x 2 2 c
3
1 2 1
1 2
2 3 u du
2
2 x 2 2 x 2 c
1
3

x2
b) Hence find; 1 x 3
dx
x2 2 3x 2
1 x 3
dx
3 2 1 x 3
dx
2
1 x3 c
3
ii x 2 x 2 dx OR x 2 x 2 dx u 2 x2
1 du
2 x 2 x 2 dx 1 u 2x
2 du dx
2
du 2 xdx
2 x 2 2 c
3
1 2 1
1 2
2 3 u du
2
2 x 2 2 x 2 c
1 1 2 2
3
3 u c
2 3

x2
b) Hence find; 1 x 3
dx
x2 2 3x 2
1 x 3
dx
3 2 1 x 3
dx
2
1 x3 c
3
ii x 2 x 2 dx OR x 2 x 2 dx u 2 x2
1 du
2 x 2 x 2 dx 1 u 2x
2 du dx
2
du 2 xdx
2 x 2 2 c
3
1 2 1
1 2
2 3 u du
2
2 x 2 2 x 2 c
1 1 2 2
3
3 u c
2 3
2 x 2 2 x 2 c
1
3

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