Find the derivative of f(x) = x^2 − 2 at x = 10 - Vidyadip

Question

Find the derivative of $f(x) = x^2 − 2$ at $x = 10$

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Answer

We have, $\text{f(x)}=\text{x}^{2}-2$ $\because\text{f}\text{(a)}=\lim\limits_{\text{h}\rightarrow0}\frac{\text{f}\text{(a+h)}-\text{f(a)}}{\text{h}}$ $\text{f}'(10)=\lim\limits_{\text{h}\rightarrow0}\frac{\text{f(10+h)}-\text{f(10)}}{\text{h}}$ $=\lim\limits_{\text{h}\rightarrow0}\frac{\text{(10+h)}^{2}-2-98}{\text{h}}$ $=\lim\limits_{\text{h}\rightarrow0}\frac{100+20\text{h}+\text{h}^{2}-100}{\text{h}}$ $=\lim\limits_{\text{h}\rightarrow0}\frac{\text{h(20+h)}}{\text{h}}$ $=\lim\limits_{\text{h}\rightarrow0}(20+\text{h})$ $\therefore\text{f}'(10)=20$

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