Purchase Solution

Calculus questions on differentiation

Not what you're looking for?

Ask Custom Question

A circle of radius 3 inches is inside a square with 12-inch sides (see figure below). How fast is the area between the circle and square changing if the radius is increasing at 4 inches per minute and the sides are increasing at 2 inches per minute?

Find dy/dx in two way (a) by differentiating implicitly and (b) by explicitly solving for y and then differentiating. Then find the value of dx/dy at the given point using your results from both the
implicit and the explicit differentiation.

x^2+5y^2=45, point: (5, 2)

Find dy/dx using implicit differentiation and then find the slope of the line tangent to the graph of the equation at the given point.
y^2-5xy+x^2+21=0 point: (2, 5)

Find dy/dx in two ways: (a) by using the "usual" differentiation patterns and (b) by using logarithmic differentiation.
y=cos^7⁡〖(2x+5)〗

use logarithmic differentiation to Find dy/dx
y=(cos⁡(x) )^x

Purchase this Solution

Solution Summary

This posting includes step by step solutions to some questions on related rates, differentiation, implicit differentiation and slope of tangent lines.

Solution Preview

1. A circle of radius 3 inches is inside a square with 12-inch sides (see figure below). How fast is the area between the circle and square changing if the radius is increasing at 4 inches per minute and the sides are increasing at 2 inches per minute?

Solution:

Let the side of square be x, radius of circle be r and the area between square and circle be A.

Area between the ...

Solution provided by:
Education
  • BSc, Meerut University
  • MSc, Meerut University
  • MPhil, Institute of Advanced Studies
  • MSc, AIT
Recent Feedback
  • "Perfect, thank you so much!!! I will definitely request you in the future! You are amazing!"
  • "Thank you. "
  • "Thank you so much I have two more that I need your help with if your available."
  • "Thank you, I was wondering why you rejected me the first time."
  • "Thanks again."
Purchase this Solution


Free BrainMass Quizzes
Multiplying Complex Numbers

This is a short quiz to check your understanding of multiplication of complex numbers in rectangular form.

Geometry - Real Life Application Problems

Understanding of how geometry applies to in real-world contexts

Exponential Expressions

In this quiz, you will have a chance to practice basic terminology of exponential expressions and how to evaluate them.

Graphs and Functions

This quiz helps you easily identify a function and test your understanding of ranges, domains , function inverses and transformations.

Probability Quiz

Some questions on probability