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Derivatives — MATHS STD 11 Science — Question

Gujarat BoardEnglish MediumSTD 11 ScienceMATHSDerivatives2 Marks
Question
Find the derivative of f(x) = 3x at x = 2
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Answer

We have, $\text{f(x)} = 3\text{x}$ $\because \text{f}'(\text{a}) = \lim\limits_{\text{h} \rightarrow0} \frac{\text{f(a+h)}-\text{f(a)}}{\text{h}}$ $\therefore \text{f}'\text{(a)}=\lim\limits_{\text{h}\rightarrow0}\frac{\text{f(2+h)}-\text{f(2)}}{\text{h}}$ $=\lim\limits_{\text{h}\rightarrow0}\frac{3(2\text{+h})-6}{\text{h}}$ $=\lim\limits_{\text{h}\rightarrow0}\frac{\text{3h}}{\text{h}}$ $=\lim\limits_{\text{h}\rightarrow0} 3$ $\therefore\text{f}'{(2)}=3$

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