1. Use the adiabatic relation for an ideal gas:

$PV^{\gamma} = \text{constant}$

2. Differentiate both sides:

$d(PV^{\gamma}) = 0$

Using product differentiation,

$V^{\gamma} \, dP + P \, d(V^{\gamma}) = 0$

Now,

$d(V^{\gamma}) = \gamma V^{\gamma-1} dV$

So,

$V^{\gamma} dP + P\gamma V^{\gamma-1} dV = 0$

3. Divide throughout by $PV^{\gamma}$:

$\frac{dP}{P} + \gamma \frac{dV}{V} = 0$

Therefore,

$\frac{dP}{P} = -\gamma \frac{dV}{V}$

4. The fractional change in pressure is $\dfrac{dP}{P}$, hence

$\boxed{\frac{dP}{P} = -\gamma \frac{dV}{V}}$

5. Check options:

• A: $-\dfrac{1}{\gamma}\dfrac{dV}{V}$ ❌
• B: $-\gamma \dfrac{V}{dV}$ ❌ (dimensionally incorrect)
• C: $-\gamma \dfrac{dV}{V}$ ✅
• D: $\dfrac{dV}{V}$ ❌

Hence, the correct option is C.