find the differential

Question

Let y=5√x 
Find the change in y, Δy when x=3 and Δx=0.4
Find the differential dy when x=3 and dx=0.4

Answer 1

Differentiating y = 5√x:

 

y' = 5/(2√x)

 

y' is also dy/dx;

 

dy/dx = 5/(2√x)

 

Substituting the values:

 

dy/0.4 = 5/(2√3)

 

dy = (5*0.4)/(2√3)

 

dy = 1/√3 = √3/3

 

*dy is also the same as Δy*