Chain Rule

Chain Rule

Postby Guest » Wed Mar 06, 2019 4:24 pm

Could someone kindly help me with this question?

The price P of an electronic component is known to be: P(c) = 2c - 18/c where c is the manufacturer's cost to produce it. The cost c is a function time t according to c(t) = 9 + 3/t Determine the rate of change of price with respect to time (dP/dt) at time t = 3 years.
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Re: Chain Rule

Postby HallsofIvy » Tue Mar 12, 2019 9:15 am

dP/dc= 2+ 18/c^2 and dc/dt= -3/t^2. When t= 3, c= 9+ 3/3= 10. dP(10)/dc= 2+ 18/100= 218/100 and and dc/dt= -3/9= -1/3. dP/dt= (218/100)(-1/3)= -218/300.

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