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
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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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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 ...
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