Find the derivative of x at x = 1. - Vidyadip

Question

Find the derivative of x at x = 1.

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Answer

Let $\text{f}(\text{x})=99\text{x}$. Accordingly, $\text{f}'(100)=\lim\limits_{\text{h}\rightarrow0}\frac{\text{f}(100+\text{h})-\text{f}(100)}{\text{h}}$ $=\lim\limits_{\text{h}\rightarrow0}\frac{99(100+\text{h})-99(100)}{\text{h}}$$=\lim\limits_{\text{h}\rightarrow0}\frac{99\times100+99\text{h}-99\times100}{\text{h}}$
$=\lim\limits_{\text{h}\rightarrow0}\frac{99\text{h}}{\text{h}}$ $=\lim\limits_{\text{h}\rightarrow0}(99)=99$ Thus, the derivative of at x = 100 is 99.

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