Answer:
see explanation
Step-by-step explanation:
Given f(x) then the derivative f'(x) is
f'(x) = lim ( h tends to zero ) [tex]\frac{f(x+h)-f(x)}{h}[/tex]
= lim ( h to 0 ) [tex]\frac{2(x+h)^2-(x+h)-(2x^2-x)}{h}[/tex]
= lim ( h to zero ) [tex]\frac{2(x^2+2hx+2h^2)-x-h-2x^2+x}{h}[/tex]
= lim ( h to zero ) [tex]\frac{2x^2+4hx+2h^2-h-2x^2}{h}[/tex]
= ( lim h to 0 ) [tex]\frac{4hx+2h^2-h}{h}[/tex]
= ( lim h to 0 ) [tex]\frac{2h(2x+h)-h}{h}[/tex]
= lim ( h to 0 ) [tex]\frac{2h(2x+h)}{h}[/tex] - [tex]\frac{h}{h}[/tex] ← cancel h on numerator/ denominator of both
= lim( h to 0 ) 2(2x + h) - 1 ← let h go to zero
f'(x) = 4x - 1
