Question

Find the derivative :f(x) = x³ - 1/x² + 2 √x -3/x

Answer 1

Okay, here we have this:

We need to find the derivative of the following function:

`\begin{gathered} f(x)=x^(3)\: -\: 1/x^(2)\: +\: 2\: √(x)\: -3/x​ \\ y=x^(3)\: -\: 1/x^(2)\: +\: 2\: √(x)\: -3/x​ \end{gathered}`

We obtain the following:

`\begin{gathered} (d)/(dx)\mleft(y\mright)=(d)/(dx)\mleft(x^3-(1)/(x^2)+2√(x)-(3)/(x)\mright) \\ =(d)/(dx)\mleft(x^3\mright)-(d)/(dx)\mleft((1)/(x^2)\mright)+(d)/(dx)\mleft(2√(x)\mright)-(d)/(dx)\mleft((3)/(x)\mright) \\ =3x^2-\mleft(-(2)/(x^3)\mright)+(1)/(√(x))-\mleft(-(3)/(x^2)\mright) \\ (dy)/(dx)=3x^2+(2)/(x^3)+(1)/(√(x))+(3)/(x^2) \end{gathered}`