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Calculus questions on differentiation

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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

https://brainmass.com/math/functional-analysis/calculus-questions-differentiation-614124

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 Summary

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

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