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Find the derivative of $4x^2-12x+9$ 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 $4x^2-12x+9$. Substituting $f(x+h)$ and $f(x)$ on the limit, we get
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$\lim_{h\to0}\left(\frac{4\left(x+h\right)^2-12\left(x+h\right)+9-\left(4x^2-12x+9\right)}{h}\right)$
Learn how to solve definition of derivative problems step by step online. Find the derivative of 4x^2-12x+9 using the definition. Find the derivative of 4x^2-12x+9 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 4x^2-12x+9. Substituting f(x+h) and f(x) on the limit, we get. Multiply the single term -12 by each term of the polynomial \left(x+h\right). Multiply the single term -1 by each term of the polynomial \left(4x^2-12x+9\right). Add the values 9 and -9.