Find the derivatives of given functions - what percentage

Question

Exp. & Log. Functions Assignment

1. Find the derivatives of each of these functions:

a) y = ln?(2x³+7).

b) y= (3x²)/e^2x

c) y= 3^(4x+3).ln?(4x+3)

d) y= 2x²/(e^2x+ x³ )

2. Use the process of implicit differentiation to find dy/(dx) given that x²e^y-y²e^x = 0.

3. Sketch the graph of the function y = x³e^x

4. Use logarithmic differentiation to find the derivative of the function y = ((x+3)⁴.(2x²+5x)³))/√(4x-3)

5. The percentage of people who have switched to a new social network y years after it was introduced is modelled by the function

p = 100/(1+9e^-y)

a) What percentage of the people switched immediately?

b) How long did it take before 75% of the population had switched?

c) After how many years was the new network growing the fastest?

d) Sketch the function.

e) Give a possible explanation for the shape of the curve.