4.(ii)   Find the derivative of the following function from first principle. ( x-1)(x-2)

Answers (1)

f(x)=( x-1)(x-2)

Now, As we know, The derivative of any function at x is 

f'(x)=\lim_{h\rightarrow 0}\frac{f(x+h)-f(x)}{h}

f'(x)=\lim_{h\rightarrow 0}\frac{(x+h-1)(x+h-2)-(x-1)(x-2)}{h}

f'(x)=\lim_{h\rightarrow 0}\frac{x^2+xh-2x+hx+h^2-2h-x-h+2-x^2+2x+x-2}{h}

f'(x)=\lim_{h\rightarrow 0}\frac{2hx+h^2-3h}{h}

f'(x)=\lim_{h\rightarrow 0}{2x+h-3}

f'(x)=2x-3  (Answer)

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