Final Answer
Step-by-step Solution
Specify the solving method
Find the derivative of $27x^3+135x^2+225x+125$ 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 $27x^3+135x^2+225x+125$. Substituting $f(x+h)$ and $f(x)$ on the limit, we get
Learn how to solve problems step by step online.
$\lim_{h\to0}\left(\frac{27\left(x+h\right)^3+135\left(x+h\right)^2+225\left(x+h\right)+125-\left(27x^3+135x^2+225x+125\right)}{h}\right)$
Learn how to solve problems step by step online. Factor the expression 27x^3+135x^2225x+125. Find the derivative of 27x^3+135x^2+225x+125 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 27x^3+135x^2+225x+125. Substituting f(x+h) and f(x) on the limit, we get. Multiply the single term 225 by each term of the polynomial \left(x+h\right). Multiply the single term -1 by each term of the polynomial \left(27x^3+135x^2+225x+125\right). Add the values 125 and -125.