Final answer to the problem
Step-by-step Solution
How should I solve this problem?
- Find the derivative using the definition
- Integrate by partial fractions
- Product of Binomials with Common Term
- FOIL Method
- Integrate by substitution
- Integrate by parts
- Integrate using tabular integration
- Integrate by trigonometric substitution
- Weierstrass Substitution
- Prove from LHS (left-hand side)
- Load more...
Find the derivative of $x^3-3x^2+3x-1$ 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 $x^3-3x^2+3x-1$. Substituting $f(x+h)$ and $f(x)$ on the limit, we get
Learn how to solve problems step by step online.
$\lim_{h\to0}\left(\frac{\left(x+h\right)^3-3\left(x+h\right)^2+3\left(x+h\right)-1-\left(x^3-3x^2+3x-1\right)}{h}\right)$
Learn how to solve problems step by step online. Factor the expression x^3-3x^23x+-1. Find the derivative of x^3-3x^2+3x-1 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^3-3x^2+3x-1. Substituting f(x+h) and f(x) on the limit, we get. Multiply the single term 3 by each term of the polynomial \left(x+h\right). Multiply the single term -1 by each term of the polynomial \left(x^3-3x^2+3x-1\right). Add the values -1 and 1.