Differentiate f(x)={x^{3}-5 x+1}/{x^{3}}.

Question

Answer DF/DX?

Answer 1

The function f(x) = (x³ - 5x+1) / x³  .

Differentiate the function with respect to x .

df / dx = d / dx [ (x³ - 5x+1) / x³ ]

The quotient rule of derivative is    d [ u/v ] = (vu' - uv') / v² .

df / dx = [ x³ (3x² -5)  -  (x³ - 5x+1)3x² ] / (x³)²                [ derivative of  xⁿ = n x^n-1 ]        

df / dx = x²[ x (3x² -5)  -  (x³ - 5x+1)3 ] / x^6

df / dx = [ x (3x² -5)  -  (x³ - 5x+1)3 ] / x^4                      

df / dx = [ 3x³ -5x  -  (3x³ -15x+3) ] / x^4  

df / dx = [ 3x³ -5x  - 3x³ +15x -3 ] / x^4  

df / dx = [10x -3] / x^4  

So the derivative of the function f(x) = (x³ - 5x+1) / x³  is  df/dx = [10x -3] / x^4 .