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find $f^{\prime}(x)$ of $f(x)=x^{2}+2 x$
in Mathematics by Gold Status (10,269 points) | 8 views

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Solution:

$\begin{aligned} & f^{\prime}(x)=\lim _{h \rightarrow 0} \frac{f(x+h)-f(x)}{h} \\ &=\lim _{h \rightarrow 0} \frac{\left((x+h)^{2}+2(x+h)\right)-\left(x^{2}+2 x\right)}{h} \\ &=\lim _{h \rightarrow 0} \frac{x^{2}+2 h x+h^{2}+2 x+2 h-x^{2}-2 x}{h} \\ &=\lim _{h \rightarrow 0} \frac{2 h x+h^{2}+2 h}{h} \\ &=\lim _{h \rightarrow 0} 2 x+h+2 \\ &=2 x+2 \end{aligned}$

by Gold Status (10,269 points)

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