Q1
Answer
Differentiate the following with respect to $x$:
  1. $x^2\sin (x^2)$
  2. $\dfrac{4x^2 - 3}{x^3}$
  3. $\dfrac{2x\sqrt{x}}{x+1}$
  1. $2x\sin (x^2) + 2x^3\cos (x^2)$
  2. $-4x^{-2} +9x^{-4}$
  3. $\dfrac{x^{\frac{1}{2}}(x+3)}{(x+1)^2}$
Q2
Answer
Solve $|3x - 1| > x+2$.
$x < -0.25$ or $x > 1.5$
Q3
Answer
Write $\dfrac{x(3x+2)}{x^2-4}$ in partial fractions.
$3 - \dfrac{2}{x+2} + \dfrac{4}{x-2}$