| Exam Board | SPS |
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| Module | SPS FM (SPS FM) |
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| Year | 2021 |
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| Session | April |
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| Topic | Product & Quotient Rules |
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- i) Differentiate the following with respect to \(x\), simplifying your answers fully
a) \(y = e ^ { 3 x } + \ln 2 x\)
b) \(y = \left( 5 + x ^ { 2 } \right) ^ { \frac { 3 } { 2 } }\)
c) \(y = \frac { 2 x } { \left( 5 - 3 x ^ { 2 } \right) ^ { \frac { 1 } { 2 } } }\)
d) \(y = e ^ { - \frac { 8 } { 3 } x } \ln \left( 1 + x ^ { 3 } \right)\)
ii) Integrate with respect to \(x\)
\begin{displayquote}
- \(\frac { 7 } { ( 2 x - 5 ) ^ { 5 } } - \frac { 3 } { 2 x - 5 }\)
- \(\frac { 4 x ^ { 2 } + 5 x - 3 } { 2 x - 5 }\)
\end{displayquote}