Answer:
see explanation
Step-by-step explanation:
Given f(x) then the derivative f'(x) is
f'(x) = lim(h tends to 0 ) [tex]\frac{f(x+h)-f(x)}{h}[/tex]
= lim ( h to 0 ) [tex]\frac{4(x+h)^2-2-(4x^2-2)}{h}[/tex]
= lim ( h to 0 ) [tex]\frac{4(x+h)^2-2-4x^2+2}{h}[/tex]
= lim( h to 0 ) [tex]\frac{4x^2+8hx+4h^2-4x^2}{h}[/tex]
= lim( h to 0 ) [tex]\frac{8hx+4h^2}{h}[/tex]
= lim ( h to 0 ) [tex]\frac{4h(2x+h)}{h}[/tex] ← cancel h on numerator/ denominator
= lim ( h to 0 ) 4(2x + h) ← let h go to zero
f'(x) = 8x
