| Exam Board | Edexcel |
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| Module | C3 (Core Mathematics 3) |
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| Topic | Product & Quotient Rules |
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- Differentiate each of the following with respect to \(x\) and simplify your answers.
- \(\cot x ^ { 2 }\)
- \(x ^ { 2 } \mathrm { e } ^ { - x }\)
- \(\frac { \sin x } { 3 + 2 \cos x }\)
- (a) Find, as natural logarithms, the solutions of the equation
$$\mathrm { e } ^ { 2 x } - 8 \mathrm { e } ^ { x } + 15 = 0$$ - Use proof by contradiction to prove that \(\log _ { 2 } 3\) is irrational.