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Find the derivative of $b^2-12b+36$ 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 $b^2-12b+36$. Substituting $f(x+h)$ and $f(x)$ on the limit, we get
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$\lim_{h\to0}\left(\frac{\left(b+h\right)^2-12\left(b+h\right)+36-\left(b^2-12b+36\right)}{h}\right)$
Learn how to solve problems step by step online. Find the derivative of b^2-12b+36 using the definition. Find the derivative of b^2-12b+36 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 b^2-12b+36. Substituting f(x+h) and f(x) on the limit, we get. Expand \left(b+h\right)^2. Multiply the single term -12 by each term of the polynomial \left(b+h\right). Solve the product -\left(b^2-12b+36\right).