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LIMITS AND DERIVATIVES — MATHS STD 11 Science — Question

Gujarat BoardEnglish MediumSTD 11 ScienceMATHSLIMITS AND DERIVATIVES4 Marks
Question
Find the derivative of 99x at x = l00 .
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Answer

Let $\text{f}(\text{x})=\text{x}$. Accordingly, $\text{f}'(1)=\lim\limits_{\text{h}\rightarrow0}\frac{\text{f}(1+\text{h})-\text{f}(1)}{\text{h}}$ $=\lim\limits_{\text{h}\rightarrow0}\frac{(1+\text{h})-1}{\text{h}}$ $=\lim\limits_{\text{h}\rightarrow0}\frac{\text{h}}{\text{h}}$ $=\lim\limits_{\text{h}\rightarrow0}(1)$$=1$
Thus, the derivative of at x at x = 1 is 1.

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