If you put solutions, please put in the hide tags, clues and tips can be left open. I prefer solutions for checking my work rather than using them to get answers, otherwise I would be screwed on the quiz haha ~Thanks

1. Differntiate f(x) = sinx^(cos x) + cosx^(sin x)

I tried implicit differntiation.

I tried to do the ln of both sides but I can't distribute the ln amongst the + sign. ln(a+b) is not = to ln a + ln b.

So how should I handle this?

2. In a fish farm, a population of fish is introduced into a pond and harvested regularly. A model for the rate of change of the fish population is given by the equation

ÃƒÂ¢Ã‹â€ Ã¢â‚¬Â P/ÃƒÂ¢Ã‹â€ Ã¢â‚¬Â t = r

_{0}* (1 - (P(t)/P

_{c})) * P(t) - ÃƒÆ’Ã…Â¸P(t)

Where r

_{0}is the birth rate of the fish, P

_{c}is the maximum population the pond can sustain, and ÃƒÆ’Ã…Â¸ is the percentage of the population harvested.

A) What value of dP/dT corresponds to a stable population?

B) If the pond can sustain 10,000 fish, the birth rate is 5%, the harvesting rate is 4%, then find the stable population level.

C)What happens if ÃƒÆ’Ã…Â¸ is raised to 5%

~~~~~

I'm thinking for C that the population will die out, but there's nothing more than a hunch to that claim.