1.4: Differentiate exponential and trigonometric expressions

4PM1/1R/June/2022 — Question 5 · 8 marks

Differentiate with respect to x\displaystyle x:
(a) e4x(6x+2)32.\mathrm{e}^{4x}(6x+2)^{\frac{3}{2}}.
Give your answer in the form
e4x6x+2(Ax+B),\mathrm{e}^{4x}\sqrt{6x+2}(Ax+B),
where A\displaystyle A and B\displaystyle B are integers.
(5)
(b) sin 3x(2x−4)3.\frac{\mathrm{sin}\,3x}{(2x-4)^3}.
(3)