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  • Find the derivative of the following functions from first principle. x ^3 - 27

4 (i)   Find the derivative of the following functions from first principle. x ^3 -27

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best_answer

Given 

f(x)=x ^3 -27

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)^3-27-((x)^3-27)}{h}

f'(x)=\lim_{h\rightarrow 0}\frac{x^3+h^3+3x^2h+3h^2x-27+x^3+27}{h}

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

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

f'(x)=3x^2

Posted by

Pankaj Sanodiya

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