Question

Differentiate f(x) = x^2 + 2x using firts principle of derivates.

Answer 1

Answer:

First Principle of Finding Derivative:

f′(x)=limh→0f(x+h)−f(x)h  

We need to find  f′(x) , given that  f(x)=2x2−x .

Which means that  f(x+h)=2(x+h)2−(x+h)  

f′(x)=limh→0(2(x+h)2−(x+h))−(2x2−x)h  

Expand into standard polynomial form and simplify.

f′(x)=limh→0(2(x2+2x h+h2)−x−h)−2x2+xh  

f′(x)=limh→0(2x2+4x h+2h2−x−h)−2x2+xh  

f′(x)=limh→02x2+4x h+2h2−x−h−2x2+xh  

f′(x)=limh→04x h+2h2−hh  

Factor

f′(x)=limh→0h(4x+2h−1)h  

Cancel

f′(x)=limh→0[4x+2h−1]  

Direct substitution

f′(x)=4x+2(0)−1  

f′(x)=4x−1  → this is your answer