| Exam Board | OCR |
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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.
- \(\frac { 6 } { \sqrt { 2 x - 7 } }\)
- \(x ^ { 2 } \mathrm { e } ^ { - x }\)
- (i) Prove the identity
$$\sqrt { 2 } \cos ( x + 45 ) ^ { \circ } + 2 \cos ( x - 30 ) ^ { \circ } \equiv ( 1 + \sqrt { 3 } ) \cos x ^ { \circ }$$ - Hence, find the exact value of \(\cos 75 ^ { \circ }\) in terms of surds.