Solve the Problem

question 189

Short Answer

Solve the problem.
- $$\text { Show that } \mathrm { df } = - \frac { 5 \left( \mathrm { y } ^ { 7 } + \mathrm { z } \right) } { \mathrm { x } ^ { 6 } \mathrm { z } ^ { 4 } } \mathrm { dx } + \frac { 7 \mathrm { y } ^ { 6 } } { \mathrm { x } ^ { 5 } \mathrm { z } ^ { 4 } } \mathrm { dy } - \left( \frac { 4 \mathrm { y } ^ { 7 } } { \mathrm { x } ^ { 5 } \mathrm { z } ^ { 5 } } + \frac { 3 } { \mathrm { x } ^ { 5 } \mathrm { z } ^ { 4 } } \right) \mathrm { dz } \text { is exact. }$$

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Definitions:

Internal Rate of Return

A financial metric used to evaluate the profitability of an investment, representing the discount rate that makes the net present value of all cash flows equal to zero.

Net Present Value

The variance between the current value of cash coming in and the current value of cash going out over a time span.

Discount Rate

The interest rate used in determining the present value of future cash flows or in evaluating the attractiveness of an investment.

Project Cash Flows

The net amount of cash that is generated or expended by a particular project or investment, after accounting for all inflows and outflows.