Y=x^x+(sinx)^x find dy/dx

$42,606.41

Explanation:

year 1 (all the values are is $)                                                  

Initial debt                                         40,000Interest of the year (7.5%)                7.5% × 40,000 = 3,000Debt at the end of the year

        (including the interest)                     40,000 + 3,000 = 43,000

Payment at the end of the year

       (half of the debt)                               43,000 / 2 = 21,500

Debt after payment                         21,500

year 2 (all the values are is $)                                                  

Initial debt                                         21,500Interest of the year (7.5%)                7.5% × 21,500 = 1,612.50Debt at the end of the year

        (including the interest)                     21,500 + 1612.50 = 23,112.50

Payment at the end of the year

       (half of the debt)                               23,112.50 / 2 = 11,556.25

Debt after payment                         11,556.25

year 3 (all the values are is $)                                                  

Initial debt                                         11,556.25Interest of the year (7.5%)                7.5% × 11,556.25 = 866.72Debt at the end of the year

        (including the interest)                     11,556.25 + 866.72 = 12,422.97

Payment at the end of the year

       (half of the debt)                               12,422.97 / 2 = 6,211.48

Debt after payment                         6,211.48

year 4 (all the values are is $)                                                  

Initial debt                                         6,211.48Interest of the year (7.5%)                7.5% × 6,211.48 = 465.86Debt at the end of the year

        (including the interest)                     6,211.48 + 465.86 = 6,667.35

Payment at the end of the year

       (half of the debt)                               6,667.35 / 2 = 3,338.67                        

Amount paid back at the end of 4 years ($) :

21,500 + 11,556.25 + 6,211.48 + 3,338.67 = 42,606.41