Question 1 - A-Level Maths

Exam Board	SPS
Module	SPS FM (SPS FM)
Year	2021
Session	March
Topic	Differentiating Transcendental Functions

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) $y = e ^ { - \frac { 8 } { 3 } x } \ln \left( 1 + x ^ { 3 } \right)$

Express $2 \tan ^ { 2 } \theta - \frac { 1 } { \cos \theta }$ in terms of $\sec \theta$.
Hence solve, for $0 ^ { \circ } < \theta < 360 ^ { \circ }$, the equation $$2 \tan ^ { 2 } \theta - \frac { 1 } { \cos \theta } = 4$$