Question

Find $d y / d x$. $$y=x^{3}(2 x-5)^{4}$$

Name: Problem 16, Chapter 4: Calculus: Graphical, Numerical, Algebraic
Uploaded: 2021-08-28T07:27:49-08:00
Duration: 1 min 39 s
Channel: Adrian Co
Description: Find d y / d x. y=x^3(2 x-5)^4

   Find $d y / d x$.

$$y=x^{3}(2 x-5)^{4}$$

Calculus: Graphical, Numerical, Algebraic

Ross L. Finney,… 5th Edition

Chapter 4, Problem 16

Instant Answer

Solved by Expert Adrian Co

08/28/2021

Step 1

We need to find the derivative of this function. We will use the product rule and the chain rule to find the derivative. The product rule is given by $(fg)' = f'g + fg'$ and the chain rule is given by $(f(g(x)))' = f'(g(x)) \cdot g'(x)$. Show more…

Show all steps

Thanks for your feedback!

Find $d y / d x$. $$y=x^{3}(2 x-5)^{4}$$

Play audio

Feedback

Adrian Co and 81 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

Product Rule

The product rule is a fundamental concept in differentiation used when dealing with the product of two differentiable functions. It states that the derivative of a product, u(x)v(x), is u'(x)v(x) + u(x)v'(x), and is crucial for solving problems that involve functions multiplied together.

Chain Rule

The chain rule is essential for differentiating composite functions. It provides a method for taking the derivative of a function that is composed of another function, by differentiating the outer function evaluated at the inner function and then multiplying by the derivative of the inner function.

Power Rule

The power rule is a basic principle used for differentiating functions of the form x^n, where n is any real number. It states that the derivative is n*x^(n-1), enabling quick and straightforward differentiation of power functions which often appear within more complex derivative problems.

Please give Ace some feedback