Question

7th list of problems. 1. Derivative of a function of one variable. Find the derivative of the function y=4x^2+2 using the definition of a derivative (without using derivative formulas). 2. lim_{x -> 0} (tg^2 5x) / (6x sin x). 3. Find dy/dx, if y = sqrt(1-x^3) / cos^2 3x. 4. Find the inflection points of the function y = x^4 + 2x^3 + 15x - 5. Sketch the graph in the vicinity of the points of inflection. 5. Write the equations of the tangent line and normal for the function y = 3x^3 - x at x=1. 6. Find all derivatives of the second order for the function z = x log_2(xy). December 17, 2017

          7th list of problems.
1. Derivative of a function of one variable. Find the derivative of the function
y=4x^2+2 using the definition of a derivative (without using derivative
formulas).
2. lim_{x -> 0} (tg^2 5x) / (6x sin x).
3. Find dy/dx, if y = sqrt(1-x^3) / cos^2 3x.
4. Find the inflection points of the function y = x^4 + 2x^3 + 15x - 5. Sketch the
graph in the vicinity of the points of inflection.
5. Write the equations of the tangent line and normal for the function y = 3x^3 - x
at x=1.
6. Find all derivatives of the second order for the function z = x log_2(xy).
December 17, 2017

Show more…

7th list of problems.
1. Derivative of a function of one variable. Find the derivative of the function
y=4x^2+2 using the definition of a derivative (without using derivative
formulas).
2. limx -> 0 (tg^2 5x) / (6x sin x).
3. Find dy/dx, if y = sqrt(1-x^3) / cos^2 3x.
4. Find the inflection points of the function y = x^4 + 2x^3 + 15x - 5. Sketch the
graph in the vicinity of the points of inflection.
5. Write the equations of the tangent line and normal for the function y = 3x^3 - x
at x=1.
6. Find all derivatives of the second order for the function z = x log2(xy).
December 17, 2017

Added by Connor L.

Calculus: Early Transcendentals

James Stewart 8th Edition

Instant Answer

Solved by Expert Adi S

03/09/2023

Step 1

Find the derivative of the function 4r+2 using the definition of a derivative. The definition of a derivative is: $$f'(x) = \lim_{h \to 0} \frac{f(x+h) - f(x)}{h}$$ Let $f(r) = 4r + 2$. Then, $$f'(r) = \lim_{h \to 0} \frac{(4(r+h) + 2) - (4r + Show more…

Show all steps

lock

Thanks for your feedback!

7th list of problems. Derivative of a function of one variable: Find the derivative of the function y=4x^2+2 using the definition of a derivative (without using derivative formulas). lim x->0 (tg^2 5x)/(6x sin x). Find dy/dx, if y = sqrt(1-x^3)/cos^2 3x. Find the inflection points of the function y = x^4 + 2x^3 + 15x - 5. Sketch the graph in the vicinity of the points of inflection. Write the equations of the tangent line and normal for the function y = 3x^3 - x at x=1. Find all derivatives of the second order for the function z = x log2(xy). December 17, 2017

Play audio

Feedback

Powered by NumerAI

Adi S and 98 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

Recommended Videos

Recommended Textbooks

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