# arrow_back Find the derivative of $f(x)=x^{3}$.

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Find the derivative of $f(x)=x^{3}$.

Find the derivative of $f(x)=x^{3}$.

\begin{aligned} \frac{d}{d x} x^{3} &=\lim _{\Delta x \rightarrow 0} \frac{(x+\Delta x)^{3}-x^{3}}{\Delta x} . \\ &=\lim _{\Delta x \rightarrow 0} \frac{x^{3}+3 x^{2} \Delta x+3 x \Delta x^{2}+\Delta x^{3}-x^{3}}{\Delta x} \\ &=\lim _{\Delta x \rightarrow 0} \frac{3 x^{2} \Delta x+3 x \Delta x^{2}+\Delta x^{3}}{\Delta x} \\ &=\lim _{\Delta x \rightarrow 0} 3 x^{2}+3 x \Delta x+\Delta x^{2}=3 x^{2} \end{aligned}
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