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  • Find the derivative of the following functions from first principle: - x^- 1

1.(ii)   Find the derivative of the following functions from first principle: ( - x ) ^{-1}

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best_answer

Given.

f(x)= ( - x ) ^{-1}

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)^{-1}}{h}

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

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

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

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

f'(x)=\frac{1}{x^2}

 

Posted by

Pankaj Sanodiya

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