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

User Agop
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1 Answer

6 votes

+Answer:

The derivative is 2x + 2.

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.

User Abbas Mulani
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