# Differentiation and Rate of Change Word Problems

1) Differentiate the equations a) y=8/5xsquared b) y=4cosX - 3ex

2)The formula C=60=t3/12 This equation refers to a machine in a workshop. This machine costs Â£C to lease each week according to the formula and t is the number of hours per week worked by the machine. The rate of increase of cost during the week is given by dC/dt.

a) Find a general expression for dC/dt.

b) Use your expression to calculate after how many hours (t) the rate of increase of cost exceeds Â£1:50

3) Integrate the following equations y = - 2/square route of x3 and Y = x8 + x8/x8

4) s = 18 - 2t + 3.5t3 s = distance and t = seconds

1) Find the equation for the acceleration, dv/dt of the body

5) Using you equation from above find the acceleration of that body in m/s2 after the time 39.5 sec.

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#### Solution Preview

Note: Many places, it is not very clear what you meant; I am giving you different answers based on what I can infer from your questions. This should cover all possibilities.

I will use the "^" for exponents; dy/dx for derivative

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1) Differentiate the equations a) y=8/5xsquared b) y=4cosX - 3ex

Ans: a) Without proper parenthesis, there are two possibilities.

1) y = (8/5)* ...

#### Solution Summary

Rate-of-change word problems are solved and the details are provided in the solution.