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Find the derivative of $\left(2x+1\right)^3$ using the definition. Apply the definition of the derivative: $\displaystyle f'(x)=\lim_{h\to0}\frac{f(x+h)-f(x)}{h}$. The function $f(x)$ is the function we want to differentiate, which is $\left(2x+1\right)^3$. Substituting $f(x+h)$ and $f(x)$ on the limit, we get
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$\lim_{h\to0}\left(\frac{\left(2x+1\right)^3-\left(2x+1\right)^3}{h}\right)$
Learn how to solve definition of derivative problems step by step online. Find the derivative of (2x+1)^3 using the definition. Find the derivative of \left(2x+1\right)^3 using the definition. Apply the definition of the derivative: \displaystyle f'(x)=\lim_{h\to0}\frac{f(x+h)-f(x)}{h}. The function f(x) is the function we want to differentiate, which is \left(2x+1\right)^3. Substituting f(x+h) and f(x) on the limit, we get. Cancel like terms \left(2x+1\right)^3 and -\left(2x+1\right)^3. Zero divided by anything is equal to zero. The limit of a constant is just the constant.