According to given equation, we have,

y = 500e^7x + 600e^–7x

= 3500e^7x - 4200e^-7x

Now, on again differentiating we get,

= 7×3500.e^7x + 7×4200.e^-7x

= 49×500e^7x + 49×600e^-7x

= 49(500e^7x + 600e^-7x)

= 49y

Hence Proved