Final Answer
Step-by-step Solution
Specify the solving method
Find the derivative of $9-6x+x^2$ 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 $9-6x+x^2$. Substituting $f(x+h)$ and $f(x)$ on the limit, we get
Learn how to solve problems step by step online.
$\lim_{h\to0}\left(\frac{9-6\left(x+h\right)+\left(x+h\right)^2-\left(9-6x+x^2\right)}{h}\right)$
Learn how to solve problems step by step online. Find the derivative of 9-6xx^2 using the definition. Find the derivative of 9-6x+x^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 9-6x+x^2. Substituting f(x+h) and f(x) on the limit, we get. Expand \left(x+h\right)^2. Multiply the single term -6 by each term of the polynomial \left(x+h\right). Solve the product -\left(9-6x+x^2\right).