Please help .

Question

Use the definition of derivative to find the derivative of the function f(x) = (x+1)²  

Answer 1

f(x) = (x+1)² = x²+2x+1

 

f'(x) = lim_h→0[(f(x+h)-f(x))/h] 

 

       = lim_h→0[((x+h)²+2(x+h)+1 - (x²+2x+1))/h]

 

       = lim_h→0[(x²+2xh+h²+2x+2h+1-x²-2x-1)/h]

 

       = lim_h→0[(2xh+h²+2h)/h]

 

       = lim_h→0[h(2x+h+2)/h] 

 

       = lim_h→0(2x+h+2) = 2x+0+2 = 2x+2