1.4: Quotient rule and connected rates of change

0606/11/M/J/17 — Question 10 · 8 marks

(a)

Given that

y = \dfrac{\mathrm{e}^{3x}}{4x^{2} + 1}

, find

\dfrac{\mathrm{d}y}{\mathrm{d}x}

.

[3]

(b)(i)

Variables

x

,

y

and

t

are such that

y = 4\cos\left(x + \dfrac{\pi}{3}\right) + 2\sqrt{3}\sin\left(x + \dfrac{\pi}{3}\right)

and

\dfrac{\mathrm{d}y}{\mathrm{d}t} = 10

. Find the value of

\dfrac{\mathrm{d}y}{\mathrm{d}x}

when

x = \dfrac{\pi}{2}

.

[3]

(b)(ii)

Find the value of

\dfrac{\mathrm{d}x}{\mathrm{d}t}

when

x = \dfrac{\pi}{2}

.

[2]