# Calculus questions on differentiation

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

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#### 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.