Find from first principles the derivative of x squared plus 2x

+Answer:

The derivative is 2x + 2.

Step-by-step explanation:

The definition of the derivative is the limit of

[ f (x + h) ^2 - f (x) ] / h when h - --> 0.

For f (x) = x^2 + 2x:

Derivative = the limit as h - -> 0 of f (x)

= [ (x + h) ^2 + 2 (x + h) - (x^2 + 2x) ] / h

= [x^2 + 2hx + h^2 + 2x + 2h - x^2 - 2x] / h

= (2hx + 2h + h^2) / h

= 2x + 2 + h

The h can be neglected

So it is 2x + 2.