| Exam Board | WJEC |
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| Module | Further Unit 4 (Further Unit 4) |
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| Year | 2023 |
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| Session | June |
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| Topic | Differentiating Transcendental Functions |
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10. (a) By writing \(y = \sin ^ { - 1 } ( 2 x + 5 )\) as \(\sin y = 2 x + 5\), show that \(\frac { \mathrm { d } y } { \mathrm {~d} x } = \frac { 2 } { \sqrt { 1 - ( 2 x + 5 ) ^ { 2 } } }\).
(b) Deduce the range of values of \(x\) for which \(\frac { \mathrm { d } } { \mathrm { d } x } \left( \sin ^ { - 1 } ( 2 x + 5 ) \right)\) is valid.