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Find the derivative of $\left(3x-1\right)^2$ 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 $\left(3x-1\right)^2$. Substituting $f(x+h)$ and $f(x)$ on the limit, we get
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$\lim_{h\to0}\left(\frac{\left(3\left(x+h\right)-1\right)^2-\left(3x-1\right)^2}{h}\right)$
Learn how to solve definition of derivative problems step by step online. Find the derivative of (3x-1)^2 using the definition. Find the derivative of \left(3x-1\right)^2 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(3x-1\right)^2. Substituting f(x+h) and f(x) on the limit, we get. Multiply the single term 3 by each term of the polynomial \left(x+h\right). Expand \left(3x+3h-1\right)^2. The power of a product is equal to the product of it's factors raised to the same power.