Answer:
see explanation
Step-by-step explanation:
Given f(x) then the derivative f'(x) from first principles is
f'(x) = lim ( h tends to 0 ) [tex]\frac{f(x+h)-f(x)}{h}[/tex]
= lim ( h to 0 ) [tex]\frac{3(x+h)^3+2-(3x^3+2)}{h}[/tex]
= lim ( h to 0 ) [tex]\frac{3(x^3+3x^2h+3xh^2+h^3)+2-3x^3-2}{h}[/tex]
= lim ( h to 0 ) [tex]\frac{3x^3+9x^2h+9xh^2+3h^3-3x^3}{h}[/tex]
= lim ( h to 0 ) [tex]\frac{9x^2h+9xh^2+3h^3}{h}[/tex]
= lim ( h to 0 ) [tex]\frac{h(9x^2+9xh+3h^3)}{h}[/tex] ← cancel h on numerator/ denominator
= lim ( h to 0 ) 9x²+9xh+3h² ← let h go to zero
f'(x) = 9x²
