1.29: (a) Find Give your answer in the form where , and are prime numbers to be found.

4PM1/1/November/2023 — Question 8 · 8 marks

y = \frac{2\mathrm{e}^{3x+1}}{5x^2}

(a) Find

\displaystyle \frac{\mathrm{d}y}{\mathrm{d}x}

Give your answer in the form

\displaystyle \frac{Ae^{3x+1}(Bx-A)}{Cx^3}

where

\displaystyle A

\displaystyle B

and

\displaystyle C

are prime numbers to be found.

(5)

The value of

\displaystyle x

increases by 2%

(b) Use your answer to part (a) to find an estimate, in terms of

\displaystyle x

, for the percentage change in

\displaystyle y

Give your answer in the form

\displaystyle (Px - Q)

where

\displaystyle P

and

\displaystyle Q

are integers.

(3)