| Exam Board | Edexcel |
|---|
| Module | P1 (Pure Mathematics 1) |
|---|
| Year | 2018 |
|---|
| Session | Specimen |
|---|
| Topic | Chain Rule |
|---|
- Given that \(y = 4 x ^ { 3 } - \frac { 5 } { x ^ { 2 } } , x \neq 0\), find in their simplest form
- \(\frac { \mathrm { d } y } { \mathrm {~d} x }\),
- \(\int y \mathrm {~d} x\)
a) \(y = 4 x ^ { 3 } - 5 x ^ { - 2 }\)
\(\frac { d y } { d x } = 12 x ^ { 2 } + 10 x ^ { - 3 }\)
b) \(\int 4 x ^ { 3 } - 5 x ^ { - 2 } d x\)
\(= \frac { 4 x ^ { 4 } } { 4 } - \frac { 5 x ^ { - 1 } } { - 1 } + c = x ^ { 4 } + 5 x ^ { - 1 } + c\)