Find the change in y and the differential

Question

Let y= 4√x.

Find the change in y, when x=2 and the change in x is equal to 0.4=

Find the differential dy when x=2 and dx=0.4

 

Answer 1

y = 4√x = 4x^1/2

 

Use the power rule:

 

dy = 4*(1/2)x^-1/2 dx = (2/√x) dx

 

For x=2 and dx=0.4:

 

dy = (2/√2)*(0.4) = 0.8/√2

 

Rationalize the answer by multiplying it by √2/√2:

 

dy = (0.8/√2)*(√2/√2) = 0.4√2 ≅ 0.56569