Find f^'(a) f(t)=2 t^3+t

Name: Problem 32, Chapter 2: Calculus
Uploaded: 2019-06-24T12:51:34-08:00
Duration: 1 min 35 s
Channel: Allan Hungria
Description: Find f^'(a) f(t)=2 t^3+t

step 1 So if f of t is equal to 2 t cubed plus t, what we're going to do to find f prime of t, is we're

Question

Find $f^{\prime}(a)$ $$f(t)=2 t^{3}+t$$

   Find $f^{\prime}(a)$ $$f(t)=2 t^{3}+t$$

Calculus

James Stewart 8th Edition

Chapter 2, Problem 32

Instant Answer

Solved by Expert Allan Hungria

06/24/2019

Step 1

The function given is $ f(t) = 2t^3 + t $. Show more…

Show all steps

Thanks for your feedback!

Find $f^{\prime}(a)$ $$f(t)=2 t^{3}+t$$

Play audio

Feedback

Allan Hungria and 88 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

Power Rule

The power rule is a basic technique in differentiation that simplifies the process of finding the derivative of functions in the form of t^n. It states that the derivative of t^n is n*t^(n-1), and it is widely used due to its straightforward application for polynomial functions.

Evaluating the Derivative at a Point

Evaluating the derivative at a specific point involves first finding the general derivative of the function and then substituting the specific point into this derivative. This provides the instantaneous rate of change of the function at that particular point.

Differentiation

Differentiation is a fundamental concept in calculus that allows us to compute the rate at which a function is changing at any point. It involves finding the derivative, which represents the slope of the tangent line to the function's graph at a given point.

Please give Ace some feedback