Find the derivative of f(x) = 99x at x = 100 - Vidyadip

Question

Find the derivative of f(x) = 99x at x = 100

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Answer

We have, $\text{f}(\text{x}) =99\text{x}$ $\because\text{f}'\text{(a)}=\lim\limits_{\text{h}\rightarrow0}\frac{\text{f(a+h)}-\text{f(a)}}{\text{h}}$ $\text{f}'(100)=\lim\limits_{\text{h}\rightarrow0}\frac{\text{f(100+h)-f(100)}}{\text{h}}$ $=\lim\limits_{\text{h}\rightarrow0}\frac{99(100+\text{h})-9900}{\text{h}}$ $=\lim\limits_{\text{h}\rightarrow0}\frac{9900+99\text{h}-9900}{\text{h}}$ $=\lim\limits_{\text{h}\rightarrow0} 99$ $\therefore\text{f}'(100)=99$

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