1.

d. \( \frac{x^{3}+5 x^{2}+4 x+3}{x^{3}} \)

Answer»
Let f(x) =(x^3+5x^2+4x+3) /x^3
              =1+5/x+4/x^2+3/x^3

d/dx(f(x)) =d/dx(1+5/x+4/x^2+3/x^3) 
                  = 0-5/x^2-8/x^3-9/x^4
                  = -5/x^2-8/x^3-9/x^4
 

therefore the derivative is -5/x^2 - 8/x^3 - 9/x^4


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