Derivative of an equation, math

Question

Would you please help me with the derivative of this equation as my mathematics background is bit weak

1) (dxf/dt)=k∆p/(∅[ML+(1-M) xf])


2) (d(xf+ɛ)/dt)=k∆p/(∅[ML+(1-M)(xf+ɛ)])

It follows that:

3) dɛ/dt=(-k(1-M)∆pɛ)/(∅[ML+(1-M) xf ]^2 )

I am not sure how the equation jumped from 1 and 2 to three. Any suggestions how to derive this equation

Answer 1

HINT :

$\dfrac{d}{dx}\bigg(f(x)+g(x)\bigg) = \dfrac{d}{dx}f(x)+\dfrac{d}{dx}g(x)$

In your case you take $(2)-(1)$ to get the required equation ;