According to Fick's law, the diffusion of a solute across a cell membrane is given by
c'(t) = kA/v [C - c(t)}, (1)
Where A is the area of the cell membrane, V is the volume of the cell, c(t) is the concentration inside the cell at time t, C is the concentration outside the cell, and k is a constant.
If c0 represents the concentration of the solute inside the cell when t = 0, then it can be shown that
C(t) = ( c0 – C ) e^-kAt/v + c (2)
a- Use the last result to find c'(t).
b- Substitute back into Equation (1) to show that (2) is indeed the correct antiderivative of (1)

Question

According to Fick's law, the diffusion of a solute across a cell membrane is given by 
c'(t) = kA/v [C - c(t)},    (1)
Where A is the area of the cell membrane, V is the volume of the cell, c(t) is the concentration inside the cell at time t, C is the concentration outside the cell, and k is a constant.
If c0 represents the concentration of the solute inside the cell when t = 0, then it can be shown that
C(t) = ( c0 – C ) e^-kAt/v + c     (2)
a-	Use the last result to find c'(t).
b-	Substitute back into Equation (1) to show that (2) is indeed the correct antiderivative of (1)