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Differentiate the following making d y d x the subject. ( a ) 2 x y = y 3 + x 2 - x (

Differentiate the following making dydx the subject.
(a)
2xy=y3+x2-x
(b)
logy=66x
(c)
y=2x+2y2
The radius of a circle is increasing at a rate of 12cms. How fast is the area increasing at the instant
when the radius has reached 7cm?
A 15-foot ladder when it starts to slide down the wall at a rate of 2.5 feet per minute. How fast is the
base of the ladder moving the height of the ladder is 12 feet from the ground at that instant?
The cost to manufacture x cell phones in a day is
C(x)=12000+15x+x210000
The daily production level is currently x=4000 cell phones and is increasing at a rate of 125 units
per day. How fast is the average cost changing?
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