**Hey guys!**

There are two topics I am not 100% sure with, so I am asking you to please check over my homework. I did not do the best on the quizzes, so it is very important for me to get a perfect mark on these two assignments. Thank you very much for helping me out!

There are two topics I am not 100% sure with, so I am asking you to please check over my homework. I did not do the best on the quizzes, so it is very important for me to get a perfect mark on these two assignments. Thank you very much for helping me out!

*Derivative Applications*

1. A trough in the cross sectional shape of an inverted equilateral triangle is being filled at a rate of 355 cm3/min. The trough is 2 m long and has a side length of the triangle of 25 cm. How fast is the water level rising when the water is 12 cm deep? (5 marks)

2. A hotel owner knows that all 400 rooms can be rented for $85 per night. She also knows that for every $5 increase in price, 12 fewer rooms will be rented. How much should she charge per room to maximize her revenue? (5 marks)

3. A 1.85 m tall man is walking toward a 12 m tall street light at night at a rate of 2.2 m/s. How fast is the length of his shadow changing when he is 12 m from the street light? (5 marks)

4. A rectangular prism has its length increasing by 12 cm/min, its width increasing by 4 cm/min and its height increasing by 2 cm/min. How fast is it's volume changing when the dimensions are 200 cm in length, 50 cm in width and 30 cm in height? (5 marks)

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*Derivative of Exponential and Log Functions*

1) Find the derivative of the following functions.

a) y = (2^x)/(e^x)

b) f(x) = 2x ln(x^2 + 5)

c) g(x) = (lnx)/(e^(x^2+2))

2) If s(t) = ln(3t^2 + t) find the slope of the function at t = 2.

3) Find dy/dx for the function xy^2 + x lnx = 4y for x>0

4) Graph the function y = e^(-x^2)

5) Use logarithmic differentiation to find dy/dx for ((x + 1)^2(x + 3))/(square root(x^2 + 1)) at x=0

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