Final answer to the problem
Step-by-step Solution
How should I solve this problem?
- Find the derivative using the definition
- Find the derivative using the product rule
- Find the derivative using the quotient rule
- Find the derivative using logarithmic differentiation
- Find the derivative
- Integrate by partial fractions
- Product of Binomials with Common Term
- FOIL Method
- Integrate by substitution
- Integrate by parts
- Load more...
Find the derivative of $4x^3-18x^2+15x$ 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 $4x^3-18x^2+15x$. Substituting $f(x+h)$ and $f(x)$ on the limit, we get
Learn how to solve definition of derivative problems step by step online.
$\lim_{h\to0}\left(\frac{4\left(x+h\right)^3-18\left(x+h\right)^2+15\left(x+h\right)-\left(4x^3-18x^2+15x\right)}{h}\right)$
Learn how to solve definition of derivative problems step by step online. Find the derivative of 4x^3-18x^215x using the definition. Find the derivative of 4x^3-18x^2+15x 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 4x^3-18x^2+15x. Substituting f(x+h) and f(x) on the limit, we get. Multiply the single term 15 by each term of the polynomial \left(x+h\right). Multiply the single term -1 by each term of the polynomial \left(4x^3-18x^2+15x\right). Simplifying.