- a) Find \(\frac { d y } { d x }\) if \(y = 4 \ln ( 3 x )\)
b) Differentiate \(\frac { 2 x } { \sqrt { 3 x + 1 } }\) giving your answer in the form \(\frac { 3 x + c } { \sqrt { ( 3 x + 1 ) ^ { p } } }\), where \(c , p \in \mathbb { N }\) - Expand \(( x - 2 y ) ^ { 5 }\).
- What transformations could be used, and in which order, to transform the curve \(y = \sin x\) into the curve \(y = 2 \sin ( 3 x + 30 )\) ?
Find the equation of the tangent to the curve
$$y = 3 x ^ { 2 } ( x + 2 ) ^ { 6 }$$
at the point \(( - 1,3 )\), giving your answer in the form \(y = m x + c\).