Find the derivative at x = 2 of the function f(x) = 3x. - Vidyadip

Question

Find the derivative at x = 2 of the function f(x) = 3x.

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Answer

We have $f^{\prime}(2)=\lim _{h \rightarrow 0} \frac{f(2+h)-f(2)}{h}=\lim _{h \rightarrow 0} \frac{3(2+h)-3(2)}{h}$

$=\lim _{h \rightarrow 0} \frac{6+3 h-6}{h}=\lim _{h \rightarrow 0} \frac{3 h}{h}=\lim _{h \rightarrow 0} 3=3$

Therefore, derivative of the function 3x at x = 2 is 3.

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