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Find the derivative of $12a+8+a^3+6a^2$ 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 $12a+8+a^3+6a^2$. Substituting $f(x+h)$ and $f(x)$ on the limit, we get
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$\lim_{h\to0}\left(\frac{12\left(a+h\right)+8+\left(a+h\right)^3+6\left(a+h\right)^2-\left(12a+8+a^3+6a^2\right)}{h}\right)$
Learn how to solve definition of derivative problems step by step online. Factor the expression 12a+8a^36a^2. Find the derivative of 12a+8+a^3+6a^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 12a+8+a^3+6a^2. Substituting f(x+h) and f(x) on the limit, we get. Multiply the single term 12 by each term of the polynomial \left(a+h\right). Multiply the single term -1 by each term of the polynomial \left(12a+8+a^3+6a^2\right). Add the values 8 and -8.