The differentials are the change in the variables along the tangent line.
For y = f (x)

Problem 1:  Foy y = 3x²  7x + 2 find dy y = f (x), so dy = f' dx = (6x  7) dx 
Problem 2:  
Problem 3:  
Problem 4: 
Differentials are used to approximate the change in the dependent variable.
If y = f(x), and the change in x, x, is "small", then the actual change in y = y is approximately equal to dy, the differential.
Use the differential to approximate the change in
A = r² when r = 2 cm and r = 0.5 cm
Solution: Here A is function of r, A = f (r) so dA = f' (r) dr = f '(r) r
A dA = 2 r r  Now substitute in the values 
2(2)(0.5) = 2 cm² 6.28 cm²l 