Question

Calculate the derivative. $$ f(x)=2 x^{3}-3 x^{2}+5 $$

   Calculate the derivative.
$$
f(x)=2 x^{3}-3 x^{2}+5
$$

Calculus for AP

Calculus for AP

Jon Rogawski & Ray… 2nd Edition

Chapter 3, Problem 21

Instant Answer

Solved by Expert Foster Wisusik

12/14/2019

Step 1

The power rule states that the derivative of $x^n$ is $n*x^{n-1}$. So, for the first term $2x^3$, we bring the 3 out front and multiply it by 2, and then decrease the power by 1. For the second term $-3x^2$, we bring the 2 out front and multiply it by -3, and then Show more…

Show all steps

lock

Thanks for your feedback!

Calculate the derivative. $$ f(x)=2 x^{3}-3 x^{2}+5 $$

Play audio

Feedback

Powered by NumerAI

Foster Wisusik and 89 other subject Calculus 1 / AB educators are ready to help you.

Ask a new question

Labs

Want to see this concept in action?

NEW

Explore this concept interactively to see how it behaves as you change inputs.

View Labs

Key Concepts

Derivative

A derivative represents the rate at which a function changes with respect to a variable. It is fundamentally the slope of the tangent line to the function at any given point and is central to understanding instantaneous rates of change in calculus.

Power Rule

The power rule is a basic differentiation technique that simplifies finding the derivative of functions in the form x^n. According to the rule, the derivative of x^n is given by n*x^(n-1), making it a quick and efficient method for handling polynomial terms.

Polynomial Function

A polynomial function is a mathematical expression consisting of variables raised to non-negative integer powers and multiplied by coefficients, combined together by addition or subtraction. These functions are typically smooth and continuously differentiable, which makes them ideal for applying differential calculus techniques such as the power rule.

Recommended Videos

Transcript

Ace is your personal tutor. It breaks down any question with clear steps so you can learn.

Start Using Ace

Continue solving this problem

Create a free account to:

View full step-by-step solution
Ask follow-up questions with Ace AI
Save progress and study later