Question

Can you help me answer these 3 questions please. I'm supposed find their derivatives

Answer 1

`f^(\prime)(x)=(x^2-3)/(x^2)`

Step-by-step explanation:

Given the function f(x) defined as follows:

`f(x)=(x^2+3)/(x)`

We use the quotient rule to differentiate this.

`\text{Quotient Rule:}(v(du)/(dx)-u(dv)/(dx))/(v^2)`

From f(x):

`\begin{gathered} u=x^2+3,(du)/(dx)=2x \\ v=x,(dv)/(dx)=1 \end{gathered}`

Therefore:

`\begin{gathered} f^(\prime)(x)=(x(2x)-(x^2+3))/(x^2) \\ =(2x^2-x^2-3)/(x^2) \\ f^(\prime)(x)=(x^2-3)/(x^2) \end{gathered}`