Find the derivative of x^2– 2 at x = 10. - Vidyadip

Question

Find the derivative of $x^2– 2$ at $x = 10$.

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Answer

Let. $\text{f}(\text{x})=\text{x}^2-2$ Accordingly, $\text{f}'(10)=\lim\limits_{\text{h}\rightarrow0}\frac{\text{f}(10+\text{h})-\text{f}(10)}{\text{h}}$ $=\lim\limits_{\text{h}\rightarrow0}\frac{\big[(10+\text{h})^2-2\big]-(10^2-2)}{\text{h}}$$=\lim\limits_{\text{h}\rightarrow0}\frac{10^2+2.10.\text{h}+\text{h}^2-2-10^2+2}{\text{h}}$
$=\lim\limits_{\text{h}\rightarrow0}\frac{20+\text{h}^2}{\text{h}}$ $=\lim\limits_{\text{h}\rightarrow0}(20+\text{h})=(20+0)=20$ Thus, the derivative of $x^2 – 2$ at $x = 10$ is $20$.

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