Calculus - Derivatives?

Question

1) Find the derivative of the function y= 4x - 1 by the delta method. 
dy/dx = 

2) Find the derivative of the function y= 5/x by the delta method. 
dy/dx= 

If you could show your work that would be great. Thank you!

Answer 1

1) The equation is y = 4x - 1.

Delta Method or First Principle:

Assume h represents small change, then change in x is from x to (x+h)

i.e., x + h - x = h means that the change in x is always the small change.

Then change in y is from y (x )to y (x + h).

Therefore dy /dx = 4.

2) The equation is y = 5/x.

Therefore dy /dx = -5/x².