Final Answer
Step-by-step Solution
Specify the solving method
Find the derivative of $x^3-6x^2+12x-8$ 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 $x^3-6x^2+12x-8$. Substituting $f(x+h)$ and $f(x)$ on the limit, we get
Learn how to solve definition of derivative problems step by step online.
$\lim_{h\to0}\left(\frac{\left(x+h\right)^3-6\left(x+h\right)^2+12\left(x+h\right)-8-\left(x^3-6x^2+12x-8\right)}{h}\right)$
Learn how to solve definition of derivative problems step by step online. Find the derivative of x^3-6x^212x+-8 using the definition. Find the derivative of x^3-6x^2+12x-8 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 x^3-6x^2+12x-8. 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(x^3-6x^2+12x-8\right). Add the values -8 and 8.